Question Video: Using the Properties of Similarity to Find the Value of an Unknown in Two Triangles Mathematics

Video Transcript

Triangle 𝐴𝐵𝐶 and 𝐴 prime 𝐵 Prime 𝐶 Prime in the given figure are similar. Work out the value of 𝑥. Here we can see that 𝐴 and 𝐴 prime are congruent. The reason why is because these two triangles are similar. And in similar triangles, their corresponding angles are congruent. So the two angles are corresponding or go together would be 𝐴 and 𝐴 prime. So in order to find the value of 𝑥, we need to set 𝐴 and 𝐴 prime equal to each other.

So we take five 𝑥 plus 90 divided by six and set it equal to three 𝑥 plus 320 divided by six. Our first step is to get rid of the dominators, so we multiply both sides by six. And when doing so, the sixes just cancel. So we have five 𝑥 plus 90 equals three 𝑥 plus 320. Let’s go ahead and subtract three 𝑥 from both sides to get 𝑥 on the left-hand side of the equation. Five 𝑥 minus three 𝑥 is two 𝑥. And on the right-hand side, the three 𝑥 is cancelled. So we have two 𝑥 plus 90 equals 320. Our next step would be to subtract 90 from both sides of the equation. The 90s cancel on the left-hand side, so we just have two 𝑥 on the left. And then on the right, 320 minus 90 is 230. So our last step would be to divide both side by two. The twos cancel on the left. And on the right, 230 divided by two is 115, so the value of 𝑥 is 115.