Question

look at this square:
1 mm
1 mm
if the side lengths are quadrupled, then which of the following statements about its area will be true?
the new area will be 16 times the old area.
the new area will be 64 times the old area.

Explanation:

Step1: Calculate the original area

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 1\) mm, the original area \(A_{old}=1^2=1\) \(mm^2\).

Step2: Calculate the new side - length

If the side - length is quadrupled, the new side - length \(s_{new}=4\times1 = 4\) mm.

Step3: Calculate the new area

Using the area formula \(A = s^2\) again, with \(s = 4\) mm, the new area \(A_{new}=4^2 = 16\) \(mm^2\).

Step4: Find the ratio of new area to old area

The ratio \(\frac{A_{new}}{A_{old}}=\frac{16}{1}\)

Answer:

The new area will be 16 times the old area.