Answer:
- The width = x = 14
- The length = x+5 = 14+5 = 19
Step-by-step explanation:
Let l = length, w = width, A = area = l×w , and P = perimeter = 2(l+w)
Let 'x' be the width
As the length 'l' of a rectangle is 5 inches more than its width.
so the length will be = x+5
As the Area of the rectangle is equal to 2 inches more than 4 times the perimeter.
A = 4P + 2
so the equation becomes
l × w = 4×2(l+w)+2
substituting w=x, l = x+5,
(x+5)x = 8(x+5+x)+2
x²+5x = 8(5+2x)+2
x²+5x = 40+16x+2
x²+5x = 16x+42
x²+5x-16x-42 =0
x²-11x-42=0
solving
similarly solving
so
x = 14, or x = -3
As the width 'x' can not be negative.
so x = 14
Thus,
- The width = x = 14
- The length = x+5 = 14+5 = 19