Question

in the diagram below, \\( \triangle gfe \sim \triangle dce \\). 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 \(\triangle GFE\sim\triangle DCE\), the ratios of corresponding sides are equal. That is \(\frac{GF}{DC}=\frac{GE}{DE}\).

Step2: Substitute the known values

We know \(GF = 48\) m, \(GE=50\) m, \(DE = 75\) m. Let \(DC=b\). Then \(\frac{48}{b}=\frac{50}{75}\).

Step3: Solve the proportion for \(b\)

Cross - multiply: \(50b=48\times75\). First, calculate \(48\times75 = 3600\). Then \(b=\frac{3600}{50}\).

Answer:

\(b = 72\) meters