Question

the figures below are similar. the labeled sides are corresponding.
2 in 8 in
$p_1 = 14$ in $p_2= $ ?
what is the perimeter of the larger rectangle?
$p_2 = \square$ inches

Explanation:

Step1: Find the scale factor

The corresponding sides of the similar rectangles are 2 in and 8 in. The scale factor \( k \) is the ratio of the side of the larger rectangle to the smaller one. So, \( k=\frac{8}{2} = 4 \).

Step2: Use the property of similar figures (perimeter ratio)

For similar figures, the ratio of their perimeters is equal to the scale factor. Let \( P_1 \) be the perimeter of the smaller rectangle and \( P_2 \) be the perimeter of the larger one. We know \( P_1 = 14 \) in. So, \( \frac{P_2}{P_1}=k \). Substituting the values, we get \( P_2=P_1\times k \).

Step3: Calculate \( P_2 \)

Substitute \( P_1 = 14 \) and \( k = 4 \) into the formula: \( P_2=14\times4 = 56 \).

Answer:

56