Question

look at this square: 8 m 8 m if the side lengths are doubled, then which of the following statements about its perimeter will be true? the new perimeter will be 4 times the old perimeter. the new perimeter will be 1/2 of the old perimeter. the new perimeter will be 2 times the old perimeter. the new perimeter will be 3 times the old perimeter.

Explanation:

Step1: Recall perimeter formula for square

The perimeter formula of a square is $P = 4s$, where $s$ is the side - length of the square. Let the original side - length be $s_1$ and the original perimeter be $P_1=4s_1$.

Step2: Find new side - length and perimeter

If the side - length is doubled, the new side - length $s_2 = 2s_1$. Then the new perimeter $P_2=4s_2$. Substitute $s_2 = 2s_1$ into the formula, we get $P_2 = 4\times(2s_1)=8s_1$.

Step3: Compare new and old perimeters

We know that $P_1 = 4s_1$ and $P_2=8s_1$. So, $\frac{P_2}{P_1}=\frac{8s_1}{4s_1}=2$. The new perimeter is 2 times the old perimeter.

Answer:

The new perimeter will be 2 times the old perimeter.