Question

triangle abc is similar to triangle def. find the measure of side ef. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. Let \(EF = x\). The proportion is \(\frac{BC}{EF}=\frac{AB}{DE}\). Substituting the values \(BC = 60\), \(AB = 45\), \(DE=6.9\), we get \(\frac{60}{x}=\frac{45}{6.9}\).

Step2: Cross - multiply

Cross - multiplying gives \(45x=60\times6.9\).

Step3: Solve for \(x\)

First, calculate \(60\times6.9 = 414\). Then \(x=\frac{414}{45}\). Simplifying \(\frac{414}{45}=\frac{414\div9}{45\div9}=\frac{46}{5}=9.2\).

Answer:

\(9.2\)