Question

the figures below are similar. the perimeter of each figure is given.

$p_1 = 12$ mm \t\t $p_2 = 16$ mm

what is the ratio of the side length of the smaller square to the side length of the larger square?

write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Find side lengths using perimeter formula

For a square, perimeter \(P = 4s\). For the smaller square with \(P_1=12\) mm, \(s_1=\frac{P_1}{4}=\frac{12}{4}=3\) mm. For the larger square with \(P_2 = 16\) mm, \(s_2=\frac{P_2}{4}=\frac{16}{4}=4\) mm.

Step2: Calculate the ratio

The ratio of the side length of the smaller square to the larger square is \(s_1:s_2 = 3:4\).

Answer:

\(3:4\)