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?
10 cm
12 cm
20 cm
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 of \(AB\) to \(JK\) (where \(JK = 5\) cm and \(AB=15\) cm). The ratio \(r=\frac{AB}{JK}=\frac{15}{5} = 3\).

Step2: Use the ratio to find \(BC\)

We know that \(NJ = 4\) cm and \(BC\) corresponds to \(NJ\). Using the similarity ratio \(r = 3\), we have \(BC=r\times NJ\). Substituting the values, \(BC = 3\times4=12\) cm.

Answer:

B. \(12\) cm