The area of a rectangular wall of a barn is 84 square feet. It's length is 12 feet longer than the width. Find the length and width of the wall of the barn.

Answer 1

width = 4.95445 ft

For the rectangular wall of the barn with an area of 84 ft²

Area = length x width

Area = 84

A = l x w

l = w + 12

A = w(w + 12)

84 = w² + 12w

Subtract 84 from both sides of the equation to get the following quadratic

0 = w² + 12w - 84

You can factor this with Quadratic Formula

(-b±sqrt(b² - 4ac))/2a

For 0 = w² + 12w - 84

a = 1

b = 12

c = -84

(-12±sqrt(12² - 4(-84)(1))))/2

(-12±sqrt(144 + 336))/2

(-12±sqrt(480))/2

(-12±(4sqrt(30)))/2

-12/2 + 4sqrt(30)2 = -6 + 2sqrt(30) = -6 + 10.95445 = 4.95445

Or

-12/2 - 4sqrt(30)/2 = -6 - 2sqrt(30) = -6 - 10.95445 = -16.95445 but width cannot be negative

So

w = 4.954445

L = w + 12 = 16.95445

Checking

A = l x w

84 = 4.95445 x 16.95445

84 = 84 (83.99997) rounded up

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