Question

in the diagram below, \\( \triangle def\sim\triangle dgh \\). find \\( b \\).

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

\\( b= \\) yards

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle DEF\sim\triangle DGH\), the ratios of corresponding sides are equal. That is \(\frac{b}{77.4}=\frac{25.8}{81}\).

Step2: Solve for \(b\)

Cross - multiply: \(81b = 77.4\times25.8\).
First, calculate \(77.4\times25.8 = 77.4\times(25 + 0.8)=77.4\times25+77.4\times0.8=(70 + 7.4)\times25+(70+7.4)\times0.8=(70\times25+7.4\times25)+(70\times0.8 + 7.4\times0.8)=(1750+185)+(56 + 5.92)=1935+61.92 = 1996.92\).
Then, \(b=\frac{1996.92}{81}=24.65333\cdots\approx24.6\).

Answer:

\(24.6\)