Question

if both dimensions are tripled, then which of the following will be true? the new perimeter will be 3 times the old perimeter. the new perimeter will be 1/2 of the old perimeter. 3 in 6 in

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. For the original rectangle with $l = 6$ in and $w = 3$ in, $P_{old}=2(6 + 3)=18$ in.

Step2: Find new dimensions

If both dimensions are tripled, the new length $l_{new}=3\times6 = 18$ in and the new width $w_{new}=3\times3 = 9$ in.

Step3: Calculate new perimeter

Using the perimeter formula, $P_{new}=2(18 + 9)=2\times27 = 54$ in.

Step4: Compare new and old perimeters

$\frac{P_{new}}{P_{old}}=\frac{54}{18}=3$. So the new perimeter is 3 times the old perimeter.

Answer:

The new perimeter will be 3 times the old perimeter.