Find the length and width of the wall of the barn.

Question

The area of a rectangular wall of a barn is 192 square feet. Its length is 88 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

This appears to be a strange wall! If width is W, then length is 2W + 88. Area is length X width, which is 192 sq. ft.

So the equation is (W)(2W + 88) = 192, or 2W^2 + 88W = 192, or 2W^2 + 88W - 192 = 0.

Solving with solution to quadratic equation gives:

W = {(-88) + SQRT(88^2 - [4][2][-192])} / (2)(2).

W = {(-88) + SQRT(7744 + 1536)} / 4 ={ (-88) + SQRT(9280)} / 4 = (-88 + 96.33) / 4

W = 8.33 / 4 = 2.083

Length = 2(2.083) + 88 = 4.166 + 88 = 92.166

Check: Area = 92.16 X 2.083 = 191.97