Question

△abc ~ △def
find the value of x.

x = ?

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), the ratios of their corresponding sides are equal. That is \(\frac{BC}{EF}=\frac{AC}{DF}\).

Step2: Substitute the known values

We know \(BC = 9\) ft, \(AC=15\) ft, \(DF = 5\) ft, and \(EF=x\) ft. Substituting into the ratio \(\frac{9}{x}=\frac{15}{5}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(15x=9\times5\). Then \(15x = 45\). Divide both sides by 15: \(x=\frac{45}{15}\).

Answer:

\(x = 3\)