Question

the figures below are similar. the labeled sides are corresponding.
8.1 m
7.2 m
$p_1 = ?$
$p_2 = 27.2$ m
what is the perimeter of the larger rectangle?
$p_1 = \square$ meters

Explanation:

Step1: Find the scale factor

Since the figures are similar, the ratio of their corresponding sides is the scale factor. Let the scale factor be \( k \), so \( k=\frac{8.1}{7.2} \). Simplifying, \( k = \frac{9}{8} \).

Step2: Use the scale factor for perimeters

For similar figures, the ratio of perimeters is equal to the scale factor. Let \( P_1 \) be the perimeter of the larger rectangle and \( P_2 = 27.2 \) m be the perimeter of the smaller one. Then \( \frac{P_1}{P_2}=k \), so \( P_1 = P_2\times k \). Substituting the values, \( P_1 = 27.2\times\frac{9}{8} \).

Step3: Calculate \( P_1 \)

First, \( 27.2\div8 = 3.4 \), then \( 3.4\times9 = 30.6 \). So \( P_1 = 30.6 \) meters.

Answer:

\( 30.6 \)