Question

given: \\(\triangle efg \sim \triangle ihg\\) with measures as marked. calculate the length of \\(d\\). round answer to nearest tenth, if needed. \\(d = \square\\) m

Explanation:

Step1: Identify corresponding sides

Since \(\triangle EFG \sim \triangle IHG\), the ratios of corresponding sides are equal. So, \(\frac{EF}{IH}=\frac{FG}{HG}\).

Step2: Substitute known values

We know \(EF = d\), \(IH = 180\) m, \(FG = 78\) m, \(HG = 45\) m. Substituting into the proportion: \(\frac{d}{180}=\frac{78}{45}\).

Step3: Solve for \(d\)

Cross - multiply: \(45d=180\times78\). Then, \(d = \frac{180\times78}{45}\). First, \(180\div45 = 4\), so \(d=4\times78 = 312\).

Answer:

\(312\)