Question

triangle rst is similar to triangle uvw. find the measure of side uv. figures are not drawn to scale.

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. Let \(UV = x\). The ratio of \(RT\) to \(UW\) is equal to the ratio of \(RS\) to \(UV\). So, \(\frac{RT}{UW}=\frac{RS}{UV}\).

Step2: Substitute the known values

We know \(RT = 6\), \(UW=35.6\), \(RS = 3\). Substituting into the proportion \(\frac{6}{35.6}=\frac{3}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(6x=3\times35.6\).

Step4: Solve for \(x\)

First, calculate \(3\times35.6 = 106.8\). Then \(x=\frac{106.8}{6}\).
\(x = 17.8\)

Answer:

\(17.8\)