Question

The area of a rectangular wall of a barn is 192 sq. Ft. It's length is 8 ft. Longer than twice it's width. Find the length and width of the wall of the barn?

Answer 1

Answer: length = 24 ft

Width = 8 ft

Step-by-step explanation:

Let L represent the length of the barn.

Let W represent the width of the barn.

The area of a rectangular wall of a barn is 192 sq. Ft. This means that

LW = 192- - - - - - - - - - - - - - -1

It's length is 8 ft longer than twice it's width. This means that

L = 2W + 8

Substituting L = 2W + 8 into equation 1, it becomes

W(2W + 8) = 192

2W² + 8W = 192

2W² + 8W - 192 = 0

Dividing through by 2, it becomes

W² + 4W - 96 = 0

W² + 12W - 8W - 96 = 0

W(W + 12) - 8(W + 12) = 0

(W - 8)(W + 12) = 0

W = 8 or W = - 12

Since the width cannot be negative, then W = 8

L = 192/W = 192/8

L = 24