Math Puzzles 🔥

[00:00:33]All right, guys. This is the very first question we need to solve for the value of x.

[00:00:40]So, take your time, think about it, and give your answer along with the correct approach.

[00:00:45]We're going to solve for the value of x.

[00:00:47]Hi Kushagra, thanks for joining.

[00:00:52]We're solving for the value of x.

[00:00:55]Take your time, think about it, and give your answer. Once I will be having any one of the user to give the correct answer, then we'll move to the next.

[00:01:05]Let's see who's going to give the correct answer first.

[00:02:35]>> Hi Sushila, thanks for joining.

[00:02:46]Guys, we are solving for the value of x.

[00:02:48]So, give your answer for the value of x.

[00:02:49]It has been more than 2 minutes already.

[00:02:53]You guys have taken so much of time.

[00:02:55]>> Hi Sushila, thanks for joining.

[00:03:03]>> So, anyone with the correct answers?

[00:03:17]All right, Kushagra is saying blue angles are 45 each.

[00:03:22]Okay.

[00:03:52]Okay.

[00:03:53]Kushagra is saying the yellow angle using angle sum property is 75, which means uh the angle X is 75, right?

[00:04:02]Okay, let's see if it is 75 or not.

[00:04:08]Sushila is saying the same.

[00:04:12]Let's see, guys.

[00:04:14]See, these two angles are marked equal, which means these two angles are marked with the same color. They are equal in measure. So, if this is a right angle, these two angles are going to be 45 each.

[00:04:25]We have these two angles, I can solve for this angle, right, using the straight angle property, right?

[00:04:31]So, this much angle is going to be 65 because all of these three angles together is going to be equal to 180°.

[00:04:39]So, now I have these two angles already, like this is 40, this is 65.

[00:04:43]I can use the angle sum property here and solve for the value of X. So, X + 40 + 65 is going to be equal to 180° and therefore the value of X is going to be how much? It's going to be 75.

[00:04:59]So, 75 is the correct answer. Sushila and Kushagra, you guys were correct.

[00:05:04]We'll move to the next one. Let's have the next one. Let's see how many of you can do that.

[00:05:10]Just a minute.

[00:05:17]Let's have this.

[00:05:19]We are given with a hemisphere. I hope it is visible to all of you.

[00:05:23]We are given with a hemisphere and you are going to solve for the curved surface Take your time. Think about it.

[00:05:40]Let's see who's going to give the answer first. You are going to give your answer in terms of pi only. Don't give your answer in decimals.

[00:06:13]Black winter is here. Your answer for the first question is correct.

[00:06:18]We are at the question number two, where we need to solve for the curved surface area.

[00:06:42]Okay, Kushagra is saying 98 pi.

[00:06:46]Using CSA formula of hemisphere.

[00:06:51]We'll see if it is 98 pi or not.

[00:06:56]Anyone guys? Anyone with the same answer?

[00:07:11]We need to solve for the CSA.

[00:07:22]Sushila is also saying the same. Black winter is also saying the same 98 pi, which is 308. Okay.

[00:07:31]Just a minute, guys.

[00:08:13]>> All right.

[00:08:14]See, we know the formula for the S uh curved surface area of hemisphere is 2 pi r squared, right? I'll substitute the value of r here, which is 7.

[00:08:25]So, it's going to be 7 squared. 2 pi 7 squared is going to be 49 into 2, which is going to give me 98 pi.

[00:08:31]And if you want to uh substitute the value of pi as 22 by 7, you'll be getting 308.

[00:08:37]So, 98 pi or 308, both are correct.

[00:08:40]We'll have the next one, guys.

[00:08:42]Let's see how many of you can solve this.

[00:08:47]Now, this is something else. We need to solve for the area of triangle ABC.

[00:08:52]Let's see how many of you can do this.

[00:08:57]We are given with the side length of AC as 4.

[00:09:01]The side AD and the side CD are marked equal.

[00:09:06]And you are going to solve for the area of triangle ABC. Take your time. Give your answer along with the correct approach. Let's see how many of you can do this.

[00:10:27]>> Anyone, guys?

[00:10:31]Okay, Black Winter is has given his answer.

[00:10:37]He's saying A is equals to area is 6 root 3. Okay, let's see if it is correct or not.

[00:10:47]See, guys, what what I can do, first of all, if I'll mark the this angle as theta, like this is also theta, right? So, if this is theta, as these two sides are equal, so this angle is also going to be theta.

[00:11:00]I can solve for the value of theta because 2 theta plus theta plus this 90 is going to be equal to 180 degrees, right? So, the value of theta is going to be 30 degrees.

[00:11:10]Correct? So, let's just mark this as 30 degree.

[00:11:13]Now, if this is 30 degree, I can solve for this side and this side also, right?

[00:11:17]Using tan or I can say sine, right?

[00:11:21]So, AB upon 4, which is going to be perpendicular upon hypotenuse, is equals to sine 30. Sine 30 is 1 by 2.

[00:11:30]Right?

[00:11:31]And from here, I'll be getting AB as two.

[00:11:35]So, the value of AB is two.

[00:11:37]Similarly, if I'm going to use AB upon BC, this is going to be tan theta where tan theta is 30. So, tan 30 is going to be 1 by root three.

[00:11:48]And I can solve for the value of BC here because AB is two. So, BC is going to be two root three.

[00:11:54]So, we have this BC as two root three.

[00:11:57]Now, we have the base and I can say the base or we can say the length of the two legs. So, the area is going to be half into product of the length of the legs, which is going to half into base into height.

[00:12:10]So, it's two root two two root three into this two. So, two two will get cancelled out. You are left with two root three.

[00:12:17]So, the area is going to be two root three.

[00:12:21]Black Ranger has given his answer and his answer is correct.

[00:12:25]The only person to give the answer.

[00:12:26]We'll move to the next guys. Let's have the next one.

[00:12:32]Let's have this.

[00:12:36]Let's see who's going to give the answer for this one guys. We need to solve for the shaded region area that is the blue shaded area.

[00:12:44]Uh lengths are already given.

[00:12:47]This AE is given as two A.

[00:12:50]This length EB is four. This is A plus two, which is AD.

[00:12:56]And this segment CD is given to you as two.

[00:12:59]One more thing is given to you that the area of AED and BCDE is same.

[00:13:07]They are equal.

[00:13:09]Their areas are equal.

[00:13:12]So, take your time, think about it.

[00:13:14]Let's see how many of you can do this.

[00:15:24]>> Mhm.

[00:16:17]>> Okay, then who is here?

[00:16:21]He's given his explanation for this.

[00:16:33]What is the value of A?

[00:16:47]Black Avenger has given his explanation.

[00:16:51]Let's see, guys. What is given to us?

[00:16:54]We'll use that only, right? This is given to us. We'll use this and equate the areas. Area of AED is given to you. So, we'll use half into base into height. It's going to be A into A plus two because this two will get cancelled out with the base with the half.

[00:17:12]Right?

[00:17:13]This is equal to area of BCD.

[00:17:17]So, BCD can be calculated the BCDE, which is this angle, with this area BCDE.

[00:17:25]So, this is going to be the area of triangle bigger triangle the uh minus the area of the smaller triangle, right? The area of the bigger triangle is going to be how much? It's going to be this side length is going to be A plus four because two plus two will get added up.

[00:17:38]And this is going to be 2A plus four.

[00:17:41]So, it's going to be half into base into height. This two will get cancelled out.

[00:17:44]We'll be left with A plus two into A plus four minus the area of this triangle, which is same as this, right?

[00:17:54]So, it's going to be A plus two into A only.

[00:17:59]Now, if I'm going to rearrange this and I'll get a quadratic equation, which is already mentioned by Black Avenger in the comments.

[00:18:07]You'll get the value of A. The value of A is going to be four. So, once you get the value of A, you can solve for the area.

[00:18:14]The area is going to be A plus two into four.

[00:18:21]Right?

[00:18:22]Again, you can you have the value of A.

[00:18:25]You can substitute the value directly here. You can solve for the sides also.

[00:18:29]Like this is going to be four plus two, six.

[00:18:32]This is going to be uh four twos are eight.

[00:18:37]So, now you have everything. You can solve for the area. The area is going to be 24. 24 is the right answer. Black Avenger, you have Black Avenger, the only one.

[00:18:48]No one else has given the correct answer. TNO has given the correct explanation by the way, but not the answer.

[00:18:56]Okay, guys. We'll move to the next.

[00:18:58]Let's have this.

[00:19:01]This is easy, I think. You guys can give it a try. We need to solve for the value of B and A and hence find the ratio B by A.

[00:19:11]Let's see who's going to give the answer first.

[00:19:43]Guys, it is given that the given figure is a square.

[00:19:47]It's mentioned over there.

[00:21:34]>> Guys, anyone?

[00:21:37]We need to solve for B by A.

[00:21:39]Or we can say B ratio A.

[00:23:13]>> What happened guys? This is you are taking so much of time.

[00:23:17]This is easy.

[00:23:25]Anyone with the correct answer guys? Or else I should give the explanation then.

[00:23:34]I'll wait for one more minute.

[00:25:42]>> Hi Victory, thanks for joining.

[00:25:45]Uh Sushila saying only answers. What does that mean?

[00:25:53]Sushila, what What you are trying to say?

[00:26:21]Guys, it has been more than 5 minutes, I think. You've taken so much of time for this.

[00:26:27]>> [snorts] >> I'm just waiting for one user to give the correct answer along with the correct explanation, so that we can move to the next.

[00:27:12]>> Uh, victory, I can't see the answers without explanation today.

[00:27:16]I already mentioned that whenever we are doing a long format questions, it's not rapid fire. I do need the explanation and I prefer the comments with the explanations.

[00:27:29]So, I'll let you know whether answer your answer is correct or not.

[00:27:33]But, I'll still wait for someone to give the explanation for that.

[00:29:32]>> All right, Kushagra has given the explanation. Let's see guys if it is correct or not. See.

[00:29:39]Uh, we do have this side length which is B and this is A, right? So, the entire side of this square is going to be A + B, so I can mark this as A + B.

[00:29:49]So, I can take this triangle first of all because these two triangles are going to be definitely going to be similar to each other because two of the angles, one is theta, theta, and another is right angle, right? So, they are going to be similar.

[00:30:04]So, I can equate the corresponding sides.

[00:30:06]So, what I'll I'll be getting I'll can write A by A like this, perpendicular upon hypotenuse. [snorts] It's going to be A by A.

[00:30:15]Is equal to perpendicular upon hypotenuse of this triangle. So, perpendicular here is A + B upon hypotenuse is 15.

[00:30:25]So, I have taken these two triangles, this one and this one.

[00:30:28]Okay?

[00:30:29]So, when I'm going to simplify this, I'll be getting a relation like 15A is equals to 8A + 8B, which is same as mentioned by Kushagra.

[00:30:38]So, this is this is going to be 7A is equals to 8b.

[00:30:43]Therefore, b by a is going to be 7 by 8.

[00:30:46]So, b by a is 7 by 8.

[00:30:49]7 ratio 8 is the right answer. Black Avenger, you are also correct.

[00:30:54]You use He used cos and then okay.

[00:30:58]One the same thing.

[00:31:00]Basics of trigonometric ratios.

[00:31:03]We get the answer as 7 by 8. 7 by 8 is the right answer. Victory B, your answer is also correct.

[00:31:09]Kushagra and Black Avenger, you are also correct. We'll have the next question.

[00:31:14]Let's have this.

[00:31:17]And this is going to be the last question for today, guys.

[00:31:20]Let's see who's going to give the correct answer for this. We need to solve for the value of x. Two of the sides are already marked equal, AB and BC.

[00:31:28]AD is 8 and CD is 10.

[00:31:33]So, give your answers along with the correct explanation. You You need not to give the step-by-step explanation, but ex- I'm just expecting you to comment your approach.

[00:31:59]Bye, Victory. Have a good night.

[00:33:48]>> Um Six is not the correct answer, guys.

[00:33:52]You need to check your logic and if you're writing it six, you need to give your answer along with the explanation.

[00:34:09]However, six is not the correct answer for this.

[00:34:13]Because this side this length can't be eight.

[00:34:19]Because this much length is marked as eight. So, if these two sides are equal, then they must be marked equal also, right?

[00:34:27]So, BC can't be eight, so therefore X can't be six.

[00:34:56]>> Okay, Prakash is here. Prakash is saying 4.24.

[00:35:00]Guys, whatever the your answers is just throw your explanation for that the or your approach, a bit of your approach so that I can get to know what you are thinking about the problem.

[00:35:12]However, 4.24 is not the correct answer.

[00:35:20]Check your logic.

[00:36:42]>> Yes Kushagra, but six is not the correct answer and I gave you the reason why it can't be six. I hope it is clear to you.

[00:36:50]I'm just waiting for one of the user to give the correct answer or then I'm going to give the explanation soon.

[00:36:58]So just be there.

[00:37:57]Guys, is there anyone Guys, I've taken so much of time already.

[00:38:04]Does angle A and C are equal? Definitely they are going to be equal because ABC is an isosceles triangle.

[00:38:11]Base angle of an isosceles triangle are equal.

[00:40:19]>> Guys, are you on it?

[00:40:23]Or should I give the explanation then?

[00:41:52]All right, guys. I can't give you that much of time. I'm going to give the explanation. See here.

[00:41:57]What is happening here? How are we going to solve this?

[00:42:02]See, this is an isosceles triangle. And if I'm going to drop a perpendicular from this point B on side AC, definitely this perpendicular is going to bisect this entire side AC. Right?

[00:42:16]This is going to bisect AC. Now, the length of the AC is going to be 18.

[00:42:20]Right? Which means up to here, if I'm going to mark this point as P, this AP is going to be nine.

[00:42:28]And similarly, this PC is also going to be nine.

[00:42:32]Correct? Which means this DP is going to be a one unit. Right?

[00:42:38]And PC is nine. I already wrote it.

[00:42:41]Now, see.

[00:42:42]What else I can do? I can mark this angle as something. Let's say I'm marking this as theta.

[00:42:49]Now, if this is theta, see, this angle is also going to be theta. How it is possible?

[00:42:56]See, this is theta, so this is going to be 90 minus theta. This angle is already a right angle. Correct? So, definitely, this is going to be theta.

[00:43:05]I'm going to erase this. I hope it is clear that if this is theta, this is also going to be theta.

[00:43:12]So, we have everything now.

[00:43:14]So, in this two triangle, I can say like BPD, this triangle, this smaller triangle BPD. I'll use some other color.

[00:43:20]This triangle.

[00:43:22]The smaller one.

[00:43:24]Is similar to this bigger triangle, which is CBD, this entire triangle, this one.

[00:43:31]They're similar.

[00:43:32]Right? So, I can write the corresponding sides in same proportion.

[00:43:36]Correct? So, let's say for I'm writing for the smaller triangle, it's perpendicular upon the hypotenuse of this triangle.

[00:43:44]So, it's going to be 1 upon X.

[00:43:47]Is equal to Similarly, for the bigger triangle, I can write perpendicular for the bigger triangle is going to be X.

[00:43:54]And the hypotenuse for the bigger triangle is going to be this DC.

[00:43:58]This DC is of length 10 units. So, it's going to be X by 10.

[00:44:04]And on cross multiplication, I'll be getting X squared is equal to 10 one are 10, right? Therefore, the value of x is going to be root of 10.

[00:44:13]So, the correct answer for this is root of 10. I hope it is clear to every one of you guys.

[00:44:21]>> [snorts] >> Anyone with any doubt, they can ask.

[00:44:53]Black Avenger is here. He has given the answer already.

[00:44:57]Your answer and explanation is correct, Black Avenger.

[00:45:01]Thanks for that.

[00:45:03]Okay, guys. For rest of the user, I hope it is clear.

[00:45:10]Yes, this was the good one.

[00:45:13]But, Victory we already left the chat before solving this.

[00:45:18]Okay, guys.

[00:45:19]I'll see you tomorrow at the same timing. Till then, take care. Bye-bye.

[00:45:22]Have a good night.

[00:45:27]Bye, everyone.

[00:45:38]Bye, Sushila.

[00:45:39]Bye, Kishant.

[00:46:00]Bye, Black Avenger. Have a good night.

[00:46:02]Bye, everyone.