Question

triangle ghi is similar to triangle jkl.
what is the length of gi?
10
30
49
79

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle GHI\sim\triangle JKL\), the ratios of corresponding sides are equal. That is \(\frac{GH}{JK}=\frac{HI}{KL}=\frac{GI}{JL}\).
We know \(HI = 10\), \(KL=30\), \(JL = 90\). Let \(GI=x\).

Step2: Set up the proportion

Using \(\frac{HI}{KL}=\frac{GI}{JL}\), substitute the values: \(\frac{10}{30}=\frac{x}{90}\).
Cross - multiply: \(30x=10\times90\).

Step3: Solve for \(x\)

\(30x = 900\), then \(x=\frac{900}{30}=30\).

Answer:

\(30\)