The area of a rectangular wall of a barn is 140 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

For a rectangle, area is length times width:

A = LW

If "length is 6 feet longer than twice its width", then L = 6 + 2W

Plugging "6 + 2W" into the area equation in place of "L" we get:

A = (6 + 2W)W and since the area is 140 then:

140 = (6 + 2W)W

140 = 6W + 2W²

2W² + 6W - 140 = 0

W² + 3W - 70 = 0

(W + 10)(W - 7) = 0

W + 10 = 0 meaning W = -10 or

W - 7 = 0 meaning W = 7 feet

In this case, W cannot be a negative number (width is nt negative) so W = 7

Since L = 6 + 2W then L = 6 + 2(7) = 20 feet

Answer 2

Area = L x W

L = 2W + 6

140 = (2W + 6)(W) = 2W² + 6W

2W² + 6W - 140 = 0

Divide by 2: W² + 3W - 70 = 0

Factor: (W + 10)(W - 7) = 0

W = -10 (can't happen!)

W = 7 ft (OK); L = 2(7) + 6 = 20 ft

Check: 7 x 20 = 140 sq ft