Hello! I've been wanting help with work like this? can someone help me answer and explain it to me?

Question

asked Jan 23, 2023 123k views

1 Answer

Unirgy · Answer 1 · 2023-01-27T22:31:45+0000

Given that the triangles are similar, we can deduct that RS is proportional to UV, RQ is proportional to UT.

Having said that, we can form the following proportion.

$\begin{gathered} (RS)/(UV)=(RQ)/(UT) \\ (54)/(36)=(24)/(x+5) \end{gathered}$

Then, we solve for x.

$\begin{gathered} 54(x+5)=24\cdot36 \\ x+5=(24\cdot36)/(54) \\ x+5=(864)/(54) \\ x+5=16 \\ x=16-5 \\ x=11 \end{gathered}$ Hence, x is equal to 11.