look at this square:\n\nif the side lengths are doubled, then which of the following statements about its…

look at this square:\n\nif the side lengths are doubled, then which of the following statements about its perimeter will be true?\n\nthe new perimeter will be 3 times the old perimeter.\nthe new perimeter will be 4 times the old perimeter.\nthe new perimeter will be $\frac{1}{2}$ of the old perimeter.\nthe new perimeter will be 2 times the old perimeter.

look at this square:\n\nif the side lengths are doubled, then which of the following statements about its perimeter will be true?\n\nthe new perimeter will be 3 times the old perimeter.\nthe new perimeter will be 4 times the old perimeter.\nthe new perimeter will be $\frac{1}{2}$ of the old perimeter.\nthe new perimeter will be 2 times the old perimeter.

Answer

Explanation:

Step1: Calculate original perimeter

The shape is a rectangle (labeled as square but dimensions are 3 in and 2 in). Perimeter formula: $P = 2(l + w)$ $P_{\text{old}} = 2(3 + 2) = 2 \times 5 = 10$ in

Step2: Find new side lengths

Double each side: new length $= 3 \times 2 = 6$ in, new width $= 2 \times 2 = 4$ in

Step3: Calculate new perimeter

$P_{\text{new}} = 2(6 + 4) = 2 \times 10 = 20$ in

Step4: Relate new and old perimeter

$\frac{P_{\text{new}}}{P_{\text{old}}} = \frac{20}{10} = 2$

Answer:

The new perimeter will be 2 times the old perimeter.