Question

if both dimensions are doubled, then which of the following will be true? the new perimeter will be 3 times the old perimeter. the new perimeter will be 2 1/2 of the old perimeter. the new perimeter will be 4 times the old perimeter. 3 yd 4 yd

Explanation:

Step1: Find the original perimeter

The original rectangle has length $l = 4$ yd and width $w=3$ yd. The formula for the perimeter of a rectangle is $P = 2(l + w)$. So, $P_{old}=2(4 + 3)=2\times7 = 14$ yd.

Step2: Find the new - dimensions

If both dimensions are doubled, the new length $l_{new}=2\times4 = 8$ yd and the new width $w_{new}=2\times3 = 6$ yd.

Step3: Find the new perimeter

Using the perimeter formula $P = 2(l + w)$ again, $P_{new}=2(8 + 6)=2\times14 = 28$ yd.

Step4: Compare new and old perimeters

We find the ratio $\frac{P_{new}}{P_{old}}=\frac{28}{14}=2$. So the new perimeter is 2 times the old perimeter.

Answer:

The new perimeter will be 2 times the old perimeter.