Question

quadrilateral abcd is similar to quadrilateral efgh. find ef. round answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \(ABCD\) is similar to quadrilateral \(EFGH\), the corresponding sides are proportional. So, \(AB\) corresponds to \(EF\), and \(BC\) corresponds to \(FG\).
Let \(AB = 11\), \(BC = 7\), \(FG = 26\), and \(EF = x\). The proportion is \(\frac{AB}{EF}=\frac{BC}{FG}\).

Step2: Set up the proportion

Substitute the known values into the proportion: \(\frac{11}{x}=\frac{7}{26}\).

Step3: Solve for \(x\)

Cross - multiply: \(7x = 11\times26\).
Calculate \(11\times26 = 286\), so \(7x=286\).
Then \(x=\frac{286}{7}\approx40.9\).

Answer:

\(EF\approx40.9\)