Question

the figures below are similar. the labeled sides are corresponding.
2 m
1 m
p₁ = ? p₂ = 10 m
what is the perimeter of the smaller pentagon?
p₁ = meters

Explanation:

Step1: Find the scale factor

The corresponding sides of the similar pentagons are 1 m (smaller) and 2 m (larger). So the scale factor \( k=\frac{1}{2} \).

Step2: Relate perimeters using scale factor

For similar figures, the ratio of perimeters is equal to the scale factor. Let \( P_1 \) be the perimeter of the smaller pentagon and \( P_2 = 10 \) m be the perimeter of the larger one. Then \( \frac{P_1}{P_2}=k \), so \( P_1 = P_2\times k \).
Substitute \( P_2 = 10 \) and \( k=\frac{1}{2} \): \( P_1 = 10\times\frac{1}{2}=5 \).

Answer:

5