Question

quadrilateral abcd is similar to quadrilateral efgh. find fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale. d c 5 2 a b g x f e 22 h

Explanation:

Step1: Identify Corresponding Sides

In similar quadrilaterals \(ABCD\) and \(EFGH\), corresponding sides are proportional. Side \(BC = 2\) in \(ABCD\) corresponds to side \(FG = x\) in \(EFGH\), and side \(CD = 5\) in \(ABCD\) corresponds to side \(GH = 22\) in \(EFGH\).

Step2: Set Up Proportion

Since the quadrilaterals are similar, the ratio of corresponding sides is equal. So, \(\frac{BC}{FG}=\frac{CD}{GH}\). Substituting the known values: \(\frac{2}{x}=\frac{5}{22}\).

Step3: Solve for \(x\)

Cross - multiply to get \(5x = 2\times22\). Then \(5x = 44\). Divide both sides by 5: \(x=\frac{44}{5}=8.8\).

Answer:

\(8.8\)