Question

the figures below are similar. the labeled sides are corresponding.
9 yd
7 yd
p₁ = 45 yd
p₂ = ?
what is the perimeter of the smaller pentagon?
p₂ = \boxed{} yards

Explanation:

Step1: Set up proportion for similar figures

For similar figures, the ratio of perimeters is equal to the ratio of corresponding sides. Let \(P_1 = 45\) yd (perimeter of larger pentagon), side of larger pentagon \(s_1=9\) yd, side of smaller pentagon \(s_2 = 7\) yd, and perimeter of smaller pentagon \(P_2\). The proportion is \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\).

Step2: Substitute values into proportion

Substitute \(P_1 = 45\), \(s_1 = 9\), and \(s_2=7\) into \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\), we get \(\frac{45}{P_2}=\frac{9}{7}\).

Step3: Cross - multiply to solve for \(P_2\)

Cross - multiply: \(9\times P_2=45\times7\). Then \(9P_2 = 315\). Divide both sides by 9: \(P_2=\frac{315}{9}\).

Step4: Calculate the value of \(P_2\)

\(P_2 = 35\).

Answer:

\(35\)