Question

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

Explanation:

Step1: Determine the scale factor

Since the pentagons are similar, the ratios of corresponding sides are equal. Let's find the scale factor using the sides \(JN = 3\) and \(PT = 2.1\). The scale factor from \(JKLMN\) to \(PQRST\) is \(\frac{2.1}{3}=0.7\).

Step2: Find the length of \(QR\)

The corresponding side to \(KL\) (length 6) is \(QR\) (length \(x\)). Using the scale factor, we have \(x = 6\times0.7\).
\(x = 4.2\)

Answer:

\(x = 4.2\)