Question

the figures below are similar. the labeled sides are corresponding.
3.5 m
1.2 m
p₁ = ? p₂ = 6 m
what is the perimeter of the larger pentagon?
p₁ = meters

Explanation:

Step1: Set up the proportion

Since the figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding sides. Let \(P_1\) be the perimeter of the larger pentagon. The proportion is \(\frac{P_1}{P_2}=\frac{\text{side}_1}{\text{side}_2}\), so \(\frac{P_1}{6}=\frac{3.5}{1.2}\).

Step2: Solve for \(P_1\)

Cross - multiply: \(1.2P_1 = 3.5\times6\). Then \(1.2P_1=21\). Divide both sides by \(1.2\): \(P_1=\frac{21}{1.2}\).

Step3: Calculate the value

\(P_1 = 17.5\)

Answer:

\(17.5\)