Question

the figures below are similar. the labeled sides are corresponding.

if the ratio of the squares perimeters is 13:9, what is s?

s = feet

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 side length of the green square be \(s\) and the side length of the blue square be \(1.8\) ft. The ratio of perimeters is \(13:9\), so the ratio of side lengths is also \(13:9\).
We can set up the proportion \(\frac{s}{1.8}=\frac{13}{9}\).

Step2: Solve the proportion for \(s\)

Cross - multiply: \(9s = 1.8\times13\).
First, calculate \(1.8\times13=23.4\). Then, solve for \(s\) by dividing both sides of the equation \(9s = 23.4\) by \(9\). So \(s=\frac{23.4}{9}\).
\(s = 2.6\).

Answer:

\(2.6\)