Question

if the side lengths are halved, then which of the following statements about its area will be true? the ratio of the new area to the old area will be 1:2. the ratio of the new area to the old area will be 1:4. the ratio of the new area to the old area will be 16:1. the ratio of the new area to the old area will be 1:8.

Explanation:

Step1: Calculate old - area

The old square has side length $a = 8$ cm. The area formula for a square is $A=a^{2}$. So the old area $A_{old}=8^{2}=64$ $cm^{2}$.

Step2: Calculate new - side - length

The side lengths are halved, so the new side length $a_{new}=\frac{8}{2}=4$ cm.

Step3: Calculate new - area

Using the area formula for a square again, the new area $A_{new}=4^{2}=16$ $cm^{2}$.

Step4: Find the ratio of new area to old area

The ratio $\frac{A_{new}}{A_{old}}=\frac{16}{64}=\frac{1}{4}=1:4$.

Answer:

The ratio of the new area to the old area will be 1:4.