Question

find the unknown lengths in the pair of similar triangles. a = □ mm

Explanation:

Step1: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. Let the sides of the first triangle be $14$ mm, $12$ mm, and the sides of the second triangle be $b$ and $11$ mm. The proportion is $\frac{14}{b}=\frac{12}{11}$.

Step2: Cross - multiply

Cross - multiplying gives $12b = 14\times11$.

Step3: Solve for $b$

$b=\frac{14\times11}{12}=\frac{154}{12}=\frac{77}{6}\approx12.83$ mm.

Answer:

$\frac{77}{6}$ mm