Question

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

Explanation:

Step1: Recall perimeter formula for square

The perimeter formula for a square is $P = 4s$, where $s$ is the side - length of the square. Let the original side - length be $s_1$ and the new side - length be $s_2$. Given $s_2=3s_1$.

Step2: Calculate original and new perimeters

The original perimeter $P_1 = 4s_1$. The new perimeter $P_2 = 4s_2$. Substitute $s_2 = 3s_1$ into the new - perimeter formula: $P_2=4\times(3s_1)=12s_1$.

Step3: Find the ratio of new to old perimeters

To find how many times the new perimeter is of the old perimeter, calculate $\frac{P_2}{P_1}$. Substitute $P_1 = 4s_1$ and $P_2 = 12s_1$ into the ratio: $\frac{P_2}{P_1}=\frac{12s_1}{4s_1}=3$.

Answer:

The new perimeter will be 3 times the old perimeter.