Question

look at this square: 1 in 1 in if the side lengths are tripled, then which of the following statements about its perimeter will be true? the ratio of the new perimeter to the old perimeter will be 3:1. the ratio of the new perimeter to the old perimeter will be 4:1. the ratio of the new perimeter to the old perimeter will be 2:1. the ratio of the new perimeter to the old perimeter will be 1:2.

Explanation:

Step1: Recall perimeter formula for square

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

Step2: Find old and new perimeters

Let the original side - length be $s_1 = 1$ in, so the original perimeter $P_1=4\times1 = 4$ in. If the side - length is tripled, the new side - length $s_2 = 3\times1=3$ in, and the new perimeter $P_2 = 4\times3=12$ in.

Step3: Calculate the ratio of new to old perimeter

The ratio of the new perimeter to the old perimeter is $\frac{P_2}{P_1}=\frac{12}{4}=3:1$.

Answer:

The ratio of the new perimeter to the old perimeter will be 3:1.