Question

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

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

Explanation:

Step1: Set up the proportion

Since the pentagons are similar, the ratios of corresponding sides are equal. Let's assume the ratio of \( \frac{AB}{JK}=\frac{BC}{JN}\). Here \(AB = 15\) cm, \(JK=5\) cm, \(JN = 4\) cm, and \(BC=x\) cm. The proportion is \(\frac{15}{5}=\frac{x}{4}\).

Step2: Solve the proportion

Cross - multiply: \(15\times4 = 5x\). So \(60=5x\). Then divide both sides by 5: \(x=\frac{60}{5}\).

Answer:

A. \(10\) cm