Question

learn with an example or watch a video in the diagram below, △hgf ~ △hed. find w. f 4 m e w h 3 m g 8 m d write your answer as a whole number or a decimal. do not round. w = meters submit

Explanation:

Step1: Recall Similar Triangles Property

Since \(\triangle HGF \sim \triangle HED\), corresponding sides are proportional. So, \(\frac{HG}{HE}=\frac{GF}{ED}\).

Step2: Identify Corresponding Sides

From the diagram, \(HG = 3\) m, \(GF = 4\) m, \(ED = 8\) m, and \(HE = w\). Substitute into the proportion: \(\frac{3}{w}=\frac{4}{8}\).

Step3: Solve for \(w\)

Cross - multiply: \(4w=3\times8\). Then \(4w = 24\). Divide both sides by 4: \(w=\frac{24}{4}=6\).

Answer:

\(w = 6\) meters