Question

quadrilateral abcd is similar to quadrilateral efgh. find the measure of side gh. round your answer to the nearest tenth if necessary. figures are not drawn to scale. answer attempt 1 out of 2

Explanation:

Step1: Use the property of similar quadrilaterals

Since quadrilateral \(ABCD\) is similar to quadrilateral \(EFGH\), the ratios of their corresponding sides are equal. That is \(\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{DA}{HE}\). Here, we can use \(\frac{DA}{HE}=\frac{CD}{GH}\).

Step2: Substitute the known values

We know \(DA = 19\), \(HE=60\), and \(CD = 34\). Let \(GH=x\). Then the proportion becomes \(\frac{19}{60}=\frac{34}{x}\).

Step3: Cross - multiply

Cross - multiplying gives us \(19x=34\times60\).

Step4: Solve for \(x\)

First, calculate \(34\times60 = 2040\). Then \(x=\frac{2040}{19}\approx106.3\).

Answer:

\( 106.3 \)