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: Find the similarity ratio

Since the pentagons are similar, the ratio of corresponding sides is equal. Let's assume the side \(AJ = 5\) cm in pentagon \(JKLMN\) corresponds to side \(AB=15\) cm in pentagon \(ABCDE\). The ratio of similarity \(r=\frac{AB}{AJ}=\frac{15}{5} = 3\).

Step2: Calculate the length of \(BC\)

The side \(NJ = 4\) cm in pentagon \(JKLMN\) corresponds to side \(BC=x\) cm in pentagon \(ABCDE\). Using the similarity ratio \(r = 3\), we have \(x=3\times4\).

Answer:

\(12\) cm, so the answer is B.