Question

if the ratio of the sides of two squares is 3:1, what is the ratio of their perimeters? a 3:1 b 4:1 c 9:1 d 12:1

Explanation:

Step1: Recall perimeter formula for square

The perimeter of a square $P = 4s$, where $s$ is the side - length of the square.

Step2: Let side - lengths of two squares

Let the side - lengths of the two squares be $s_1$ and $s_2$ such that $\frac{s_1}{s_2}=\frac{3}{1}$.

Step3: Calculate perimeters

The perimeters of the two squares are $P_1 = 4s_1$ and $P_2 = 4s_2$.

Step4: Find ratio of perimeters

$\frac{P_1}{P_2}=\frac{4s_1}{4s_2}=\frac{s_1}{s_2}$. Since $\frac{s_1}{s_2}=\frac{3}{1}$, the ratio of their perimeters is also $\frac{3}{1}$.

Answer:

A. 3:1