4) Look at this square:
(1) If the side lengths are halved, then which of the following statements about its area will be true?
(1) 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 $1 : 8$ .
The ratio of the new area to the old area will be $9 : 1$ .
The ratio of the new area to the old area will be $1 : 2$ .

Answer

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Answer

$1 : 4$ is the ratio of the new area to the old area.

Steps

Step 1 ：Let the original side length be $s$ , then the new side length is $\frac{s}{2}$ .

Step 2 ：Calculate the area of the original square and the new square: $s^{2}$ and ${(\frac{s}{2})}^{2}$ .

Step 3 ：Find the ratio between the new area and the old area: $\frac{{(\frac{s}{2})}^{2}}{s^{2}}$ .

Step 4 ：Simplify the ratio: $\frac{\frac{s^{2}}{4}}{s^{2}}$ = $\frac{1}{4}$ .

Step 5 ： $1 : 4$ is the ratio of the new area to the old area.