Question

the figures below are similar. the perimeter of each figure is given.

p₁ = 15 mm p₂ = 30 mm

what is the ratio of the side length of the smaller pentagon to the side length of the larger pentagon?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Recall the property of similar figures

For similar figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Step2: Calculate the ratio of perimeters

The perimeter of the smaller pentagon \(P_1 = 15\) mm and the perimeter of the larger pentagon \(P_2=30\) mm. The ratio of perimeters is \(\frac{P_1}{P_2}=\frac{15}{30}\).

Step3: Simplify the ratio

Simplify \(\frac{15}{30}\) by dividing both numerator and denominator by 15. \(\frac{15\div15}{30\div15}=\frac{1}{2}\).

Answer:

\(1:2\)