Question

look at this parallelogram: if both dimensions are quadrupled, then which of the following statements about its perimeter will be true? the new perimeter will be 2 times the old perimeter. the new perimeter will be 3 times the old perimeter. the new perimeter will be 1/2 of the old perimeter. the new perimeter will be 4 times the old perimeter.

Explanation:

Step1: Recall perimeter - change formula

For a two - dimensional shape, if the original side lengths are \(a,b,c,\cdots\) and the perimeter \(P = a + b + c+\cdots\). If each side length is multiplied by a factor \(k\), the new side lengths are \(ka,kb,kc,\cdots\) and the new perimeter \(P_{new}=k(a + b + c+\cdots)=kP\).

Step2: Identify the value of \(k\)

Here, \(k = 4\) since the dimensions are quadrupled. So the new perimeter will be \(k\) times the old perimeter, i.e., the new perimeter will be 4 times the old perimeter.

Answer:

The new perimeter will be 4 times the old perimeter.