Question

triangle bcd is similar to triangle efg. find fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Use the property of similar triangles

For similar triangles \( BCD \) and \( EFG \), the ratios of corresponding sides are equal. That is \(\frac{CD}{FG}=\frac{BC}{EF}\).
Given \( CD = 5\), \( BC=9\), \( EF = 35\), and let \( FG=x\).

Step2: Substitute values into the proportion

We have the proportion \(\frac{5}{x}=\frac{9}{35}\).
Cross - multiply to get \(9x=5\times35\).

Step3: Solve for \(x\)

\(9x = 175\), then \(x=\frac{175}{9}\approx19.4\).

Answer:

\( FG = 19.4 \)