Question

question
quadrilateral efgh is similar to quadrilateral ijkl. find the measure of side ij. round your
answer to the nearest tenth if necessary.

Explanation:

Step1: Use the property of similar quadrilaterals

Since quadrilateral \(EFGH\) is similar to quadrilateral \(IJKL\), the ratios of corresponding sides are equal. Let \(IJ = x\). Then \(\frac{EF}{IJ}=\frac{HG}{LK}\).

Step2: Substitute the known values

We know that \(EF = 11\), \(HG=9.2\), \(LK = 43\). Substituting into the proportion \(\frac{11}{x}=\frac{9.2}{43}\).

Cross - multiply gives \(9.2x=11\times43\).

Step3: Solve for \(x\)

First, calculate \(11\times43 = 473\). Then \(x=\frac{473}{9.2}\).

\(x=\frac{4730}{92}=51.413\approx51.4\)

Answer:

\(51.4\)