Question

look at this parallelogram: if both dimensions are doubled, 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 4 times the old perimeter.

Explanation:

Step1: Calculate the original perimeter

The formula for the perimeter of a parallelogram is \(P = 2(a + b)\). Here \(a=b = 1\) in (since it's a rhombus - a special case of parallelogram with all sides equal). So \(P_{old}=2(1 + 1)=4\) in.

Step2: Calculate the new perimeter

If both dimensions (sides) are doubled, \(a_{new}=b_{new}=2\) in. Then \(P_{new}=2(2 + 2)=8\) in.

Step3: Compare new and old perimeters

Find the ratio \(\frac{P_{new}}{P_{old}}=\frac{8}{4}=2\)

Answer:

The new perimeter will be 2 times the old perimeter.