Question

find r.
write your answer as a whole number or a decim

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle HIF\) and \( \triangle GEF\) are similar. Because \( \angle I=\angle GEF = 90^{\circ}\) and \( \angle F\) is common to both triangles.

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{r}{9}=\frac{16}{12}\)

Step3: Solve for \(r\)

Cross - multiply: \(12r=9\times16\). Then \(12r = 144\). Divide both sides by 12: \(r=\frac{144}{12}=12\)

Answer:

\(12\)