Question

the figures below are similar. the labeled sides are corresponding.
if the ratio of the rectangles perimeters is 3:2, what is j?
j = \boxed{} centimeters

Explanation:

Step1: Use the property of similar figures

For similar figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Let the ratio of perimeters \(P_1:P_2 = 3:2\), and the corresponding side lengths \(s_1 = 3\) cm, \(s_2=j\) cm. Then \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\).

Step2: Substitute values into the proportion

Substitute \(P_1:P_2 = 3:2\), \(s_1 = 3\) into \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\), we get \(\frac{3}{2}=\frac{3}{j}\).

Step3: Solve the proportion for \(j\)

Cross - multiply: \(3j=2\times3\).
Simplify: \(3j = 6\).
Divide both sides by 3: \(j=\frac{6}{3}=2\).

Answer:

\(2\)