Question

find f. solve for f. 4 8 6 3

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle FGH\) and \(\triangle FJI\) are similar (by AA similarity, as both have right angles and share \(\angle F\)), the ratios of their corresponding sides are equal.
The ratio of the bases is \(\frac{3}{6}\), and the ratio of the heights is \(\frac{f}{8}\).
So, \(\frac{3}{6}=\frac{f}{8}\).

Step2: Solve the proportion for \(f\)

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

Answer:

\(4\)