Question

what is the length of (overline{gi})?

Explanation:

Step1: Identify the similarity ratio

Since triangle \( GHI \) is similar to triangle \( JKL \), the ratio of corresponding sides is equal.
\(\frac{HI}{KL}=\frac{19}{38}=\frac{1}{2}\)

Step2: Use the similarity ratio to find \( GI \)

We know that \(\frac{GI}{JL}=\frac{1}{2}\), and \( JL = 64 \).
Let \( GI=x \), then \( \frac{x}{64}=\frac{1}{2} \).
Cross - multiply: \( 2x=64 \).
Solve for \( x \): \( x = 32 \).

Answer:

\(32\)