Question

the pentagons ( abcde ) and ( j k l m n ) are similar. find the length ( x ) of ( overline{kl} ).

Explanation:

Step1: Find the scale factor

Since the pentagons are similar, the ratio of corresponding sides is equal. Let's take the sides \( AE = 2 \) and \( JN = 1.6 \). The scale factor from \( ABCDE \) to \( J K L M N \) is \( \frac{1.6}{2}=0.8 \).

Step2: Calculate \( x \) using the scale factor

The corresponding side to \( BC = 5 \) is \( KL = x \). So we multiply \( BC \) by the scale factor: \( x = 5\times0.8 = 4 \).

Answer:

\( x = 4 \)