XZ= 16.25 and QR= 6.8 Since we know that both triangles are similar to one another, meaning that the corresponding sides and angles of both triangles are congruent, we also know that when dividing or multiplying by a specific value we can go from one side length to the other. What I mean by that is if you were to multiply the side length of QP by a certain value, you would get the side length of YZ, the same can be said for the other corresponding sides. Knowing that, we must first divide the side length of YX, which is 18 cm, by the side length of QP, which is 7.2 cm. When we do that, we get the value that each side of the lefthand triangle was multiplied by to create the side lengths shown in the righthand triangle. In this case, it would be 2.5. Now we just need to create an equation to represent the values we are trying to solve for. In this case, we are first trying to determine the side length of XZ. As I said before, corresponding sides of similar triangles are proportional. XZ’s corresponding side would be PR, which we know to be 6.5 cm long. Therefore, we must multiply 6.5 by 2.5 (our scaling factor) in order to get the side length of XZ, which would then be 16.25. Now, we just need to do the opposite to get the side length of QR. This time we would divide by 2.5 in order to scale our triangle down. So, the value of QR’s corresponding side is YZ, which is 17, we would then divide that by 2.5, and get 6.8 as our answer. Hopefully that cleared some things up for you.
