99% of Students FAILED to Solve this Beautiful Geometry Question?

Added: 2026-05-25

[00:00:00]Hello great mind. We'll have a very interesting geometric question here to solve, okay? Now, the question say that perimeter is 50 and we are to find um the area of this particular right angle triangle, okay? And they've given us perimeter as 50. Now, and the um height here is nine, but we don't know the values that is going to be here, okay?

[00:00:23]So, this is the base, so we can name it as B and this is the hypotenuse, so we can name it A, okay? The hypotenuse will be A, okay? So, from here, remember that perimeter is the distance round the shape and they've given us perimeter as 50, but these two values here are unknown. So, because the perimeter is the distance round the shape, we are going to have um A plus B plus nine, which is the height, equals 50.

[00:00:55]Perimeter is the distance round the shape, okay? So, from here, we are going to have um A plus B. We are trying to take transpose of this nine here by collecting like terms, so it's going to be equal to 50 minus nine, okay? So, from here, we have A plus B equals 50 minus nine is 41 and this is equation one, okay? So, from here, we we need to find the equation two and the equation two, remember that according to the Pythagorean theorem, hm?

[00:01:32]The hypotenuse The square of the hypotenuse side is equal to the sum of the square of these two sides, okay?

[00:01:40]Now, the hypotenuse side is A, so we have A squared equals um B squared plus nine squared, okay? So, from here, if we take transpose of this B squared, we are going to have A squared minus is plus here, so we are going to have minus b squared equals 9 squared is um 81, okay? So, from here, we have an algebraic algebraic identity here. So, we are going to expand this, okay? Remember that this is difference of two squares, so it's going to be a plus b open another uh parenthesis a minus b, okay? And this equal 81, okay? Now, remember that we have um let's continue over here.

[00:02:30]Now, remember that we have a plus b to be equal to 41 and we have a plus b here. So, we are going to have a plus b, which is 41, okay? Then, in parenthesis a minus b and this equals 81. Now, we are going to divide both sides of the equation by 41.

[00:02:49]This will be divided by 41, okay? Now, this will divide this and we have a minus b equals 81 divide by 41, okay?

[00:03:00]Now, this will be equation two.

[00:03:03]Now, we have equation one here, which is a plus b equals 41, and we have equation b here, okay? Now, the next thing we are going to do is to add equation two and equation one. So, we are going to have equation two plus equation equation one, okay? We are going to add these two equations together. Now, equation two is this, which is a minus b equals 81 divide by 41, okay? Now, add equation two, we are summing them together. Equation one is a plus b and that's equals 41. And this is equation two and this is equation one. Now, from here, a plus a is 2 a, okay? Then, minus b plus plus b is zero, So, this one is out, okay? And we have this to be equal to this 81 / 41. 81 / 41 plus 41, okay? Remember that we are adding them together. And this can be divided by one. Now, from here we have 2 A will be equal to the LCM between 41 and one is 41, okay? 41. Now, 41 / 41 is one. 1 * 81 is 81 plus 1 / 41 is 41. 41 * 41 will give us 1,681, okay? So, from here Okay, so from here we are going to have 2 A will be equal to 81 plus 1,681 will give us 1,762, okay? Then divide by 41. Now, from here if we cross and multiply, it simply means that we can use this two to divide 1,762.

[00:04:55]And when we do that, we are going to have 881.

[00:04:59]So, it simply means that the value of A equals 881 / 41, okay? So, we've gotten the value of um A as this, okay? So, from my equation one from equation one, okay? Now, from equation one, remember that equation one is A plus B equals 41. Now, we are going to substitute this value of A for A here, okay? But before then, let's make B the subject of formula. And B will be equal to 41 minus A, which is 881 / 41. Now, this can be divided by one as well, okay? So, let's continue over here. So, from here B will be equal to the LCM of 1 and 41 is 41, okay? Now, 1 / 41 will give us 41. 41 * this 41 will give us 1,681, okay? Then, minus 41 / 41 is 1. 1 * 881 will be 881, okay? So, from here, we are going to have that B will be equal to 1,681 - 881 will give us 800, okay? So, we have 800 / 41.

[00:06:26]So, the value of B is this and the value of A is this, okay? So, from here, remember that we are asked to find the area of the right-angled triangle, okay?

[00:06:38]And the area of a right-angled triangle is half base * height, okay? And remember that B is this. So, we are going to have the area A equals 1 / 2 * B is 800 / 41 * B H, which is the height, is 9, okay? So, from here, 2 will divide itself one. 2 / 800 will give us 400.

[00:07:06]So, we have A to be equal to 400 * 9.

[00:07:10]That is 9 * 4 will give us 36 and we'll bring the other two zero. So, it will give us 3,600 3,000 3,600, okay? / 41. Now, 3,600 / 41 will give us approximately 87.8 square units, okay? Square units. And this is the value of the area that we are expected to find in this particular question that we are given, okay? Thank you so much for watching to the end.

[00:07:46]Please do well to share this video and share your thoughts in the comment section. Bye.