Question

the figures below are similar. the labeled sides are corresponding.
1 m
$p_1 = ?$
2 m
$p_2 = 10$ m
what is the perimeter of the smaller pentagon?
$p_1 = \square$ meters

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides of similar figures is the scale factor. The corresponding sides are 1 m (smaller) and 2 m (larger), so the scale factor from smaller to larger is $\frac{1}{2}$.

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. So $\frac{P_1}{P_2}=\frac{1}{2}$.

Step3: Solve for $P_1$

Substitute $P_2 = 10$ into the equation: $P_1=\frac{1}{2}\times P_2=\frac{1}{2}\times10 = 5$.

Answer:

5