Question

If RS = 102, ST = 96, RT = 80, VW = 24, and UW = 20, find theperimeter of AUVW. Round your answer to the nearest tenth if necessary.Figures are not necessarily drawn to scale.solVwgetR

Answer 1

Two triangles are similar if the ratios of the corresponding sides are equal.

If ΔRST is similar to ΔUVW, we have that:

$\frac{RS}{UV}=\frac{ST}{VW}=\frac{RT}{UW}$

We are given the following parameters:

$\begin{gathered} RS=102 \\ ST=96 \\ RT=80 \\ VW=24 \\ UW=20 \end{gathered}$

Thus, we have that:

$\frac{102}{UV}=\frac{96}{24}=\frac{80}{20}$

Comparing the first two ratios, we have:

$\begin{gathered} \frac{102}{UV}=\frac{96}{24} \\ \frac{102}{UV}=4 \\ UV=\frac{102}{4} \\ UV=25.5 \end{gathered}$

Hence, the perimeter of ΔUVW is calculated to be:

$P=UV+VW+UW=25.5+24+20=69.5$

The perimeter is 69.5.