Question

in the figure below, \\(\overline{ef}\\) is one of the sides of a community social hall building to hold training facilities for talented children. one is interested to get the length of this side, which is parallel to \\(\overline{hg}\\). if the lengths of \\(\overline{hg}\\), \\(\overline{hd}\\), and \\(\overline{df}\\) are known and equal to 15 ft, 12 ft, and 132 ft, respectively, what is the length of \\(\overline{ef}\\)?

Explanation:

Step1: Use the similarity of triangles

Since \(EF\parallel HG\), \(\triangle HDG\sim\triangle FDE\). By the property of similar triangles, \(\frac{HG}{EF}=\frac{HD}{DF}\).

Step2: Substitute the given values

We know that \(HG = 15\) ft, \(HD=12\) ft, and \(DF = 132\) ft. Substituting into \(\frac{HG}{EF}=\frac{HD}{DF}\), we get \(\frac{15}{EF}=\frac{12}{132}\).

Step3: Solve for \(EF\)

Cross - multiply: \(12\times EF=15\times132\). Then \(EF=\frac{15\times132}{12}\).
Calculate \(15\times132 = 1980\), and \(\frac{1980}{12}=165\).

Answer:

\(165\) ft