The area of a rectangular wall of a barn is 224 square feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the barn.

Question

Find the width of the rectangular wall

Answer 1

Area = LxW = 224

L = 2xW + 12

So, using 2W+12 in place of L, the area is

(2W + 12) x W = 2W² +12W = 224

Subtract 224 from both sides to get

2W² +12W - 224 = 0

Divide all terms by 2

W² + 6W - 112 = 0

Use quadratic formula to find 2 solutions for W. a=1, b=6, c=-112

[-b +/- sqrt(b² - 4ac)] / 2a

[-6 +/- sqrt(36 - (-448))] / 2

(-6 +/- 22) / 2

Possible solutions are (-6 + 22) / 2 = 16/2 = 8 AND (-6 - 22) / 2 = -28 / 2 = -14

The only solution that works is W = 8

Area = 224 = L x W ==> 224 = L x 8 ==> 224/8 = 28 = L

L = 2xW + 12 ==> 2x8 + 12 ==> 16+12 ==> 28 meeting conditions of the problem.