Question

the figures below are similar. the labeled sides are corresponding.
8 m
6 m
p₁ = 32 m
p₂ = ?
what is the perimeter of the smaller square?
p₂ = \boxed{} meters

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides of similar figures is the scale factor. For the squares, the side of the larger square is \(8\) m and the side of the smaller square is \(6\) m. So the scale factor from the larger to the smaller square is \(\frac{6}{8}=\frac{3}{4}\).

Step2: Use the scale factor to find the perimeter of the smaller square

Since the perimeters of similar figures are in the same ratio as their corresponding sides, we can multiply the perimeter of the larger square by the scale factor. The perimeter of the larger square \(P_1 = 32\) m. So the perimeter of the smaller square \(P_2=32\times\frac{3}{4}\).
Calculating \(32\times\frac{3}{4}\), we get \(24\).

Answer:

\(24\)