Question

look at this square:
if the side lengths 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 4 times the old perimeter.

Explanation:

Step1: Calculate the original perimeter

The formula for the perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Given \(s = 91\) cm, the original perimeter \(P_{old}=4\times91 = 364\) cm.

Step2: Calculate the new side - length and new perimeter

If the side - length is quadrupled, the new side - length \(s_{new}=4\times91\) cm. The new perimeter \(P_{new}=4\times s_{new}\). Substitute \(s_{new}=4\times91\) into the formula: \(P_{new}=4\times(4\times91)=(4\times4)\times91 = 16\times91\) cm. Also, since \(P_{old}=4\times91\), we can express \(P_{new}\) in terms of \(P_{old}\) as \(P_{new}=4\times P_{old}\) (because \(P_{new}=4\times(4\times91)\) and \(P_{old}=4\times91\)).

Answer:

The new perimeter will be 4 times the old perimeter.