Question

quadrilateral bcde is similar to quadrilateral fghi. find gh. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify Corresponding Sides

Since quadrilaterals \( BCDE \) and \( FGHI \) are similar, their corresponding sides are proportional. Let's assume \( BC \) corresponds to \( FG \), and \( CD \) corresponds to \( GH \). So \( BC = 9 \), \( CD = 16 \), \( FG = 37 \), and \( GH = x \) (the side we need to find).

Step2: Set Up Proportion

The proportion for similar figures is \(\frac{BC}{FG}=\frac{CD}{GH}\). Substituting the known values: \(\frac{9}{37}=\frac{16}{x}\).

Step3: Solve for \( x \)

Cross - multiply to get \( 9x = 16\times37 \). First, calculate \( 16\times37 = 592 \). Then, \( x=\frac{592}{9}\approx65.8 \) (rounded to the nearest tenth).

Answer:

\( 65.8 \)