Question

Find the perimeter of ATUV. Round your answer to the nearest tenth if necessary.Figures are not necessarily drawn to scale.

Answer 1

Explanation

To solve the question, we will first apply a similar triangle theorem

Similar triangles are triangles that have the same shape, but their sizes may vary.

so, we can compare similar sides to get x before we get the perimeter

Thus

$\frac{SR}{VU}=\frac{QR}{TU}$

Hence

$\frac{23}{x}=\frac{20}{24}$

Solving for x

$\begin{gathered} x=\frac{23\times24}{20} \\ x=27.6 \end{gathered}$

Thus, we will have

Then the perimeter will be:

$VT+VU+TU=36+24+27.6=87.6$

Therefore, the perimeter of the triangle TUV is 87.6