Question

the figures below are similar. the labeled sides are corresponding.
$p_1 = 6$ m
$p_2 = ?$
what is the perimeter of the larger rectangle?
$p_2 = \square$ meters

Explanation:

Step1: Find the scale factor

The corresponding sides of the similar rectangles are 1 m (small) and 3 m (large). So the scale factor \( k=\frac{3}{1} = 3\).

Step2: Relate perimeters of similar figures

For similar figures, the ratio of perimeters is equal to the scale factor. Let \( P_1 = 6\) m (perimeter of small rectangle), \( P_2\) be the perimeter of large rectangle. Then \(\frac{P_2}{P_1}=k\).
Substitute \( P_1 = 6\) and \( k = 3\): \( P_2=P_1\times k=6\times3 = 18\).

Answer:

18