Janet decides to sow grass in a rectangular plot of her garden that has a length of 30 ft and height of 25 ft . It costs her \( \$ 9.50 \) per square foot for sowing the grass. If she wants to sow grass in a plot with half the base and half the height, she will have to pay \( \$ 3,562.50 \). Is this reasonable? Explain. No; if the dimensions are halved, the area is multiplied by 4 . No; if the dimensions are halved, the area is multiplied by \( 1 / 4 \). Yes; if the dimensions are halved, the area is multiplied by 2 . Yes; if the dimensions are halved, the area is multiplied by \( 1 / 4 \).

When Janet halves the dimensions of her rectangular plot, the length becomes 15 ft and the height becomes 12.5 ft. The original area is \( 30 \text{ ft} \times 25 \text{ ft} = 750 \text{ ft}^2 \). The new area after halving the dimensions is \( 15 \text{ ft} \times 12.5 \text{ ft} = 187.5 \text{ ft}^2 \). This means the area is reduced to \( \frac{1}{4} \) of the original area. The cost to sow grass on the new plot would then be \( 187.5 \text{ ft}^2 \times 9.50 \text{ dollars/ft}^2 = 1,781.25 \text{ dollars} \), making the \$3,562.50 quoted amount unreasonable, as it suggests a cost equivalent to the full area value. To avoid confusion when shrinking dimensions, remember that area scales with the square of the dimensions. When just halving a rectangle, it’s critical to double-check calculations and understand that a reduction in dimensions significantly decreases area—and hence, costs! Missing this might lead to mistakenly high expenditure expectations. Keep your dimensions in check!