Question

find gj.
g
14
32
h
f
21
i
j
gj =
submit

Explanation:

Step1: Identify Similar Triangles

Since \( HF \parallel IJ \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle GHF \sim \triangle GIJ \). So, the ratios of corresponding sides are equal: \( \frac{GH}{GI}=\frac{GF}{GJ} \).

Step2: Calculate \( GI \)

\( GI = GH + HI = 14 + 21 = 35 \). Let \( GJ = x \), \( GF = 32 \). So, \( \frac{14}{35}=\frac{32}{x} \).

Step3: Solve for \( x \)

Cross - multiply: \( 14x = 35\times32 \). Then \( x=\frac{35\times32}{14} \). Simplify: \( 35\div14 = \frac{5}{2} \), so \( x=\frac{5}{2}\times32 = 80 \).

Answer:

\( 80 \)