Question

the figures below are similar. the labeled sides are corresponding.
7.4 cm
1.4 cm
p₁ = 29.6 cm
p₂ = ?
what is the perimeter of the smaller square?
p₂ = centimeters

Explanation:

Step1: Find the ratio of corresponding sides

The ratio of the corresponding sides of the two similar squares is \(\frac{1.4}{7.4}\).

Step2: Use the property of similar figures (ratio of perimeters)

For similar figures, the ratio of their perimeters is equal to the ratio of their corresponding sides. Let \(P_2\) be the perimeter of the smaller square. We know that \(\frac{P_2}{P_1}=\frac{1.4}{7.4}\), and \(P_1 = 29.6\) cm. So \(P_2=\frac{1.4\times29.6}{7.4}\).
First, calculate \(1.4\times29.6 = 41.44\). Then, \(P_2=\frac{41.44}{7.4}=5.6\)

Answer:

\(5.6\)