Question

The ratio of the width to the length of a rectangle is 2:3, respectively. Answer each of the following. a By what percent would the area of the rectangle change if the width of the rectangle is increased by 50% and the length is increased by the same number of units?

Answer 1

The percent change in the area of the rectangle is 12.5%.

Step-by-step explanation:

To find the change in the area of the rectangle, we first need to determine the original area. Since the ratio of the width to the length is 2:3, we can assume that the width is 2x and the length is 3x, where x is a common factor. The original area is then 2x * 3x = 6x^2.

If the width is increased by 50% and the length is increased by the same number of units, the new width is 1.5 times the original width (1.5 * 2x) and the new length is 1.5 times the original length (1.5 * 3x). The new area is (1.5 * 2x) * (1.5 * 3x) = 6.75x^2.

To find the percent change in the area, we subtract the original area (6x^2) from the new area (6.75x^2), divide by the original area, and multiply by 100%. The percent change in the area is ((6.75x^2 - 6x^2) / 6x^2) * 100% = 12.5%.