Question

the pentagons abcde and j k l m n are similar. find the length x of \overline{mn}.

Explanation:

Step1: Find the scale factor

Since the pentagons are similar, the ratio of corresponding sides is equal. Consider the sides \(AB = 2\) and \(JK=1.6\). The scale factor \(k=\frac{JK}{AB}=\frac{1.6}{2}=0.8\).

Step2: Use the scale factor to find \(x\)

The side \(ED = 5\) in pentagon \(ABCDE\) corresponds to side \(NM=x\) in pentagon \(JKLMN\). Using the formula \(x = ED\times k\), substitute \(ED = 5\) and \(k = 0.8\). So \(x=5\times0.8\).

Answer:

\(x = 4\)