Question

look at this square: 8 in 8 in if the side lengths are doubled, then which of the following statements about its area will be true? the new area will be 4 times the old area. the new area will be 16 times the old area.

Explanation:

Step1: Calculate the old area

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 8\) in, the old area \(A_{old}=8^2=64\) in².

Step2: Calculate the new side - length and new area

The new side - length \(s_{new}=2\times8 = 16\) in. Using the area formula \(A = s^2\), the new area \(A_{new}=16^2=(2\times8)^2 = 2^2\times8^2\). Since \(8^2 = A_{old}\), \(A_{new}=4\times A_{old}\)

Answer:

The new area will be 4 times the old area.