Question

write your answer as a whole number or a decimal. do not round.
u = square feet
submit

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle FED\) and \( \triangle GHD\) are similar. Because \( \angle FED=\angle HGD = 90^{\circ}\) and \( \angle FDE=\angle HDG\) (vertically - opposite angles).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{FE}{GH}=\frac{DE}{DG}\). Let \(GH = u\), \(FE = 4\), \(DE = 3\), and \(DG=12\). Then the proportion is \(\frac{4}{u}=\frac{3}{12}\).

Step3: Cross - multiply and solve for \(u\)

Cross - multiplying gives \(3u=4\times12\). So, \(3u = 48\). Dividing both sides by 3, we get \(u=\frac{48}{3}\).

Answer:

\(16\)