Question

the pentagons j k l m n and p q r s t are similar. find the length x of \\( \overline { p q } \\).

Explanation:

Step1: Use the property of similar polygons

For similar polygons, the ratios of corresponding sides are equal.
$$\frac{JK}{PQ}=\frac{KL}{QR}$$

Step2: Substitute the known values

We know that \(JK = 2\), \(KL=4\), \(QR = 3.2\). Let \(PQ=x\).
$$\frac{2}{x}=\frac{4}{3.2}$$

Step3: Cross - multiply

Cross - multiplying gives us \(4x=2\times3.2\).

Step4: Solve for \(x\)

First, calculate \(2\times3.2 = 6.4\). Then \(x=\frac{6.4}{4}\).
$$x = 1.6$$

Answer:

\(x = 1.6\)