Question

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

Answer 1

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.