Question

1. pentagon j k l m n is similar to pentagon a b c d e.

what is the length of (overline{bc}) in centimeters?
a. 10 cm
b. 12 cm
c. 20 cm
d. 21 cm

Explanation:

Step1: Determine the similarity ratio

Since the pentagons are similar, the ratio of corresponding sides is equal. Let's assume the ratio is based on the pair of sides \(AJ\) (which is \(5\) cm) and \(AE\) (which is \(15\) cm). The ratio is \(\frac{15}{5}=3\).

Step2: Calculate the length of \(BC\)

The side \(KN = 4\) cm in pentagon \(JKLMN\) corresponds to \(BC=x\) cm in pentagon \(ABCDE\). Using the similarity ratio \(3\), we have \(x = 4\times3\).

Answer:

A. \(10\) cm, B. \(12\) cm, C. \(20\) cm, D. \(21\) cm.
The correct answer is B. \(12\) cm.