Question

the quadrilaterals ( jklm ) and ( pqrs ) are similar. find the length ( x ) of ( overline{pq} ).

Explanation:

Step1: Use the property of similar quadrilaterals

For similar quadrilaterals, the ratios of corresponding sides are equal.
$$\frac{JM}{PS}=\frac{JK}{PQ}$$

Step2: Substitute the known values

Given \(JM = 4\), \(PS=7.2\), \(JK = 3\), and \(PQ=x\).
$$\frac{4}{7.2}=\frac{3}{x}$$

Step3: Cross - multiply

Cross - multiplying gives \(4x=3\times7.2\).

Step4: Solve for \(x\)

First, calculate \(3\times7.2 = 21.6\). Then \(x=\frac{21.6}{4}\).
\(x = 5.4\)

Answer:

\(x = 5.4\)