Question

The area of a rectangular wall of a barn is 56 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

Let us assume width is x feet
therefore length = 2x +6
Area = x*(2x+6)
56 = 2x^2 + 6x
x^2 + 3x - 28 = 0
x^2 + 7x - 4x - 28 = 0
x(x+7)-4(x+7) = 0
(x-4)(x+7) = 0
Either x = 4 or, x = -7(but x cannot be negative)
So width = 4 feet
and length = 2x + 6 = 2*4 + 6 = 14 feet