When the side lengths of a square are halved, the area of the square becomes one quarter of the original area, thus the ratio of the new area to the old area is 1:4. therefore, option C is correct
The question concerns the area of a square when its side lengths are halved. To find the new area, we would take the original side length of the square and divide by 2. If the original side length is s, the new side length after halving would be s/2. The area of a square is calculated by side length squared, so the original area is s^2 and the new area is (s/2)^2 which simplifies to s^2/4. Therefore, the new area is 1/4 of the original area.
Comparing the two areas, the ratio of the new area to the old area is 1:4 because the factor by which the area is reduced is the square of the factor by which the side length is reduced (in this case, halved, so the scale factor squared is 1/4).
The correct answer to the original question is: B. The ratio of the new area to the old area will be 1:4.