Find The Perimeter Of This Rectangle! – Geometry Puzzle

本站添加: 2026-06-04

[00:00:00]Hello my lovelies, it's Suzanna, and today I want to show you how to solve this problem.

[00:00:05]Three identical rectangles are put together to form one large rectangle.

[00:00:12]See figure.

[00:00:13]We can see these three identical rectangles here, and they form this one large rectangle.

[00:00:22]The large rectangle has an area of 96 square centimeters. What is the perimeter of the large rectangle?

[00:00:32]So, we have to find the perimeter of this large rectangle here.

[00:00:39]Let's call this perimeter P, and how can we find it?

[00:00:44]We need the lengths of the sides of these rectangles.

[00:00:50]Let's start with this long side here. I call this side L, and because these small rectangles are all identical, this length here is also L, and this long side here is also L.

[00:01:08]And I call the short sides S, so that we have S here, here, here, and here as well.

[00:01:17]And for the perimeter, we just have to add all these lengths now.

[00:01:22]Uh let's maybe start with the long sides. How many of these do we have? We have one, two, three long sides, so it's 3L plus the short sides. We have one, two, three, four short sides, so plus 4S.

[00:01:42]And now, we only need L and S to find the perimeter then.

[00:01:49]How can we find L and S?

[00:01:51]Uh we still have one information we haven't used yet, uh that the area of the large rectangle is 96.

[00:02:01]So, how can we find the area of this large rectangle?

[00:02:06]We just have to take the length of one of the side and the length of this side and multiply these two. So, the length here is S + L then.

[00:02:21]So, [snorts] if we multiply these two, we have L times S + L that we have to write in parentheses then because we have to multiply it by this entire side.

[00:02:34]And this is then the area of this large rectangle, so it is 96.

[00:02:42]This is one equation. The problem just is we have two variables in here.

[00:02:49]So, we would need another equation, uh some connection between S and L.

[00:02:56]What do we know about L and S? Well, if we take a look at these sides here, here we have L and here we have the same length, but this is 2 S.

[00:03:10]So, we know that L has to be the same as these two S here. So, we can write this as an equation. We take L and this is equal to 1 2 2 S.

[00:03:25]And now we have two equations for two variables and we can solve the system of equations.

[00:03:35]The great thing is that we have L here in the second equation already, so we can take this L and insert it into our L's here in our first equation. So, we take the second equation and insert it into the first equation. What do we get then here?

[00:03:58]Instead of the L, we're going to write 2 S now, so we have 2 S, which is multiplied by What do we have in the parentheses?

[00:04:10]We leave S as it is, but instead of L, we're going to write 2 S here again. And on the other side, we have the 96.

[00:04:23]Um maybe let's simplify inside. Here, we have 1 S + 2 S, which is equal to 3 S, so I'm going to erase this and write 3 S here. And now, if we multiply, we have 2 S * 3 S, which is equal to 6 S squared, and this is equal to 96 then.

[00:04:49]To solve for S, let's get rid of the 6 here by dividing both sides of the equation by 6, so that this cancels out and only S squared is left here. And 96 over 6 = 16.

[00:05:08]To solve for S, let's get rid of the square here by taking the square root on both sides of the equation.

[00:05:17]If we do this, we get two solutions for our S. So, we get a first positive solution that I call S1, and a second negative solution, S2 is going to be negative. The square root of 16 is equal to 4, and then we also get the negative 4.

[00:05:39]S was the length of our short side of our rectangle.

[00:05:44]A negative length doesn't make any sense, so we write this in parentheses.

[00:05:49]We're not going to use this.

[00:05:51]But we found the length of our short side. It is 4 cm.

[00:05:58]And to find L now, we can just take our S and insert it here into the second equation to find our L then because it is just 2 * S. So, 2 * and S was 4. 2 * 4 is equal to 8. So, we also found the length of the long side. Let's take these two values, go back to the beginning where we wanted to find our perimeter.

[00:06:31]Let's insert our values. We have 3 * L is equal to 8.

[00:06:39]And S is equal to 4.

[00:06:42]And if we calculate this now, 3 * 8 = 24 + 4 * 4 = 16. So, if we add these two numbers, we get 40 in total for our perimeter. And because we had square centimeters here, this is 40 cm then for our perimeter.

[00:07:04]I'm curious how you solved this problem, so please let me know in the comments. I wish you a wonderful day, and I hope to see you in one of my next videos. Take care.