Question

The ratio of the width to the length of a rectangle is 2:3, respectively. By what percent would the area of the rectangle change if the width of the rectangle is increased by 50

Answer 1

To calculate the percent change in the area of a rectangle when the width is increased by 50%, use the formula: Percent Change = (New Area - Original Area) / Original Area * 100%. The percent change in this case is 25%.

Step-by-step explanation:

The ratio of the width to the length of a rectangle is 2:3, respectively.

To calculate the percent change in the area of the rectangle when the width is increased by 50%, we can use the formula:

Percent Change = (New Area - Original Area) / Original Area * 100%

Let's say the original width is 2x and the original length is 3x.

The original area is then 2x * 3x = 6x^2.

When the width is increased by 50%, it becomes 2.5x (1.5 times the original width).

The new area is then 2.5x * 3x = 7.5x^2.

Plugging the values into the formula for percent change, we get:

Percent Change = (7.5x^2 - 6x^2) / 6x^2 * 100%

Simplifying the equation gives:

Percent Change = (1.5x^2) / 6x^2 * 100%

Percent Change = 25%