The area of a rectangular wall of a barn is 54 square feet. It's length is 12 feet longer than twice it's width. Find the length and width of the wall of the barn.

Answer: The length of the rectangle is 18 feet while the width is 3 feet.

Step-by-step explanation: The question has already given the Area of the rectangle as 54 square feet. However we only have clues to determine the length and width. The length has been described as 12 feet longer than twice the size of the width. So if the width is given as W, then the length would be, 12 plus 2 times W. In other words, 12 + 2W. So if the area is 54, the length is 12 + 2W and the width is W, then the expression becomes

Area = L x W

54 = (2W + 12) x W

54 = 2W² + 12W

If we rearrange all terms on one side of the equation we now have,

2W² + 12W - 54 = 0

Divide all through by 2

W² + 6W - 27 = 0

We now have a quadratic equation and by factorization this becomes

(W + 9) (W - 3) = 0

W + 9 = 0 and therefore W = - 9

OR W - 3 = 0 and therefore W = 3

We know that the dimensions cannot be a negative value so we go with W = 3.

Having been given that the length is 12 feet longer than twice the width,

Length = 12 + 2 (3)

Length = 12 + 6

Length = 18

Therefore the length of the rectangle is 18 feet and the width is 3 feet.