Question

find the unknown length y in the following pair of similar triangles.

Explanation:

Step1: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So we have $\frac{15}{7.5}=\frac{11}{5.5}=\frac{19}{y}$.

Step2: Solve for y

Cross - multiply the proportion $\frac{19}{y}=\frac{15}{7.5}$. We get $15y = 19\times7.5$. Then $y=\frac{19\times7.5}{15}$.

Step3: Calculate y

$19\times7.5 = 142.5$, and $\frac{142.5}{15}=9.5$.

Answer:

$9.5$