The length of a rectangle is 6 inches more than its width. The area of the rectangle is equal to 4 inches more than 3 times the perimeter. Find the length and width of the rectangle.

Answer 1

L = length

P = Perimeter

A = Area

The length of a rectangle is 6 inches more than its width means;

L = W + 6

P = 2 ( L + W )

P = 2 ( W + 6 + W ) = 2 ( 2 W + 6 ) = 4 W + 12

A = L ∙ W

A = ( W + 6 ) ∙ W

A = W ² + 6 W

The area of the rectangle is equal to 4 inches more than 3 times the perimeter means:

A = 3 P + 4

W ² + 6 W = 3 ( 4 W + 12 ) + 4

W ² + 6 W = 12 W + 36 + 4

W ² + 6 W = 12 W + 40

Subtract 12 W to both sides

W ² - 6 W = 40

Subtract 40 to both sides

W ² - 6 W - 40 = 0

The solutions are:

W = - 4 and W = 10

Width cannot be negative so:

W = 10 in

L = W + 6 = 10 + 6 = 16 in

Check result.

L = 16 , W = 10

L = W + 6

16 = 10 + 6

Correct.

P = 2 ( L + W ) = 2 ( 16 + 10 ) = 2 ∙ 26 = 52

A = L ∙ W = 16 ∙ 10 = 160

160 = 3 ∙ 52 + 4

160 = 156 + 4

Correct.