Question

look at this rectangle: 52 yd 25 yd if both dimensions are quadrupled, then which of the following statements about its perimeter will be true? the ratio of the new perimeter to the old perimeter will be 2:1. the ratio of the new perimeter to the old perimeter will be 4:1. the ratio of the new perimeter to the old perimeter will be 3:1. the ratio of the new perimeter to the old perimeter will be 1:2.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Let the original length be $l_1=52$ yd and original width be $w_1 = 25$ yd, so the original perimeter $P_1=2(52 + 25)=2\times77 = 154$ yd.

Step2: Find new - dimensions

If both dimensions are quadrupled, the new length $l_2=4\times52 = 208$ yd and new width $w_2=4\times25 = 100$ yd.

Step3: Calculate new perimeter

The new perimeter $P_2=2(208 + 100)=2\times308 = 616$ yd.

Step4: Find the ratio of new to old perimeter

The ratio $\frac{P_2}{P_1}=\frac{616}{154}=4:1$.

Answer:

The ratio of the new perimeter to the old perimeter will be 4:1.