the length of a rectangle is 4 more than the width. if the perimeter of the rectangle is 57.2 inches find the length and the width of the rectangle

Length = 16.3 in and Width = 12.3 in

Step-by-step explanation:

Let's name L the length and W the width of the rectangle. We can then write equations describing the statements given:

"the length of a rectangle is 4 more than the width"

L = W + 4

"the perimeter of the rectangle is 57.2 inches"

2 L + 2 W = 57.2

(where we used the formula for the perimeter of the rectangle equal to twice the rectangle's length plus twice the rectangle's width)

Now we use the first equation to substitute for L in the second one:

2 ( W + 4) + 2 W = 57.2

use distributive property to remove parenthesis

2 W + 8 + 2 W = 57.2

combine like terms

4 W + 8 = 57.2

subtract 8 from both sides

4 W = 57.2 - 8 = 49.2

divide both sides by 4 to isolate W

W = 49.2 / 4 = 12.3 in

Now we use this result in the first equation we wrote, to find L

L = W + 4 = 12.3 + 4 = 16.3 in

Therefore : Length = 16.3 in and Width = 12.3 in