Question

find the perimeter of $\triangle uvw$. round your answer to the nearest tenth if necessary. figures are not necessarily draw

Explanation:

Step1: Determine similarity

Since the angles of \(\triangle TRS\) and \(\triangle VWU\) are equal (\(53^{\circ},59^{\circ},68^{\circ}\)), the triangles are similar by AA (Angle - Angle) similarity criterion.

Step2: Find the scale factor

The ratio of corresponding sides. Let's take \(\frac{VW}{TR}=\frac{36.8}{23}\).

$$ \frac{36.8}{23}=1.6 $$

Step3: Find the other sides of \(\triangle VWU\)

For side \(WU\): \(WU = 1.6\times20=32\)
For side \(VU\): \(VU = 1.6\times22 = 35.2\)

Step4: Calculate the perimeter

Perimeter \(P=36.8 + 32+35.2\)

$$ P=(36.8+35.2)+32=72 + 32=104 $$

Answer:

\(104\)