Question

find u.
write your answer as a whole number or a decimal. do not round.
u = \boxed{} feet
submit

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle IFJ\) and \( \triangle GFH\) are similar because \( \angle I=\angle G = 90^{\circ}\) and \( \angle IFJ=\angle GFH\) (vertically - opposite angles).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{IJ}{HG}=\frac{IF}{GF}\).
Substitute \(IJ = u\), \(HG = 4\), \(IF = 6\), and \(GF = 3\) into the proportion: \(\frac{u}{4}=\frac{6}{3}\).

Step3: Solve the proportion

Cross - multiply: \(3u=4\times6\).
Simplify the right - hand side: \(3u = 24\).
Divide both sides by 3: \(u=\frac{24}{3}\).

Answer:

\(u = 8\) feet