We want to find the percent of change in the perimeters of these two rectangles. Start by recalling that a percent of change is a ratio that compares the change in a quantity to the original amount. To determine the percent of change, we can use the following formula.
Percent of change =Amount of change/Original amount
Let's find the perimeter of each rectangle. The perimeter of a rectangle is the sum of 2 times the rectangle's length and 2 times its width.
Rectangle
Length, in.
Width, in.
Perimeter, in.
A
4
2
2(4) + 2(2) =12
B
2* 4 =8
2* 2=4
2(8) + 2(4) =24
We can find the amount of change by subtracting the perimeter of Rectangle A from the perimeter of Rectangle B.
Amount of change = 24in. - 12in. = 12in.
The difference between the perimeters is 12 inches. Now we can use the formula to find the percent of change. For simplicity, we will ignore the units for now.
Percent of change=Amount of change/Original amount
We want to find the percent of change in the areas of the two rectangles from Part A. We will start by finding the area of each rectangle by multiplying the length of the rectangle by its width.
Rectangle
Length, in.
Width, in.
Area, in.^2
A
4
2
4(2) =8
B
2* 4 =8
2* 2=4
8(4) =32
We can find the amount of change by subtracting the area of Rectangle A from the area of Rectangle B.
Amount of change = 32in.^2 - 8in.^2 = 24in.^2
The difference between the areas is 24 square inches. Now we can use the formula to find the percent of change. We will ignore the units again for now to keep our calculations simple.
Percent of change=Amount of change/Original amount
