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.
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.