Question

in the diagram below, △abc ~ △ade. find b.

write your answer as a whole number or a decimal. do not round.

b = meters

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle ADE\), the ratios of their corresponding sides are equal. That is \(\frac{AC}{AE}=\frac{AB}{AD}\).

Step2: Substitute the known values

We know \(AD = 9\) m, \(AB=6\) m, \(AE = 10.2\) m and \(AC=b\). Substituting into \(\frac{AC}{AE}=\frac{AB}{AD}\), we get \(\frac{b}{10.2}=\frac{6}{9}\).

Step3: Solve for \(b\)

Cross - multiply: \(9b=6\times10.2\). Then \(9b = 61.2\). Divide both sides by 9: \(b=\frac{61.2}{9}\).

Answer:

\(b = 6.8\) meters