The are of a rectangluar wall of a barn is 224 square feet. its length is 12 feet longer then twice its width. find the length and width of the wall of the barn

L x W= 224
L= 2w + 12
(2w + 12) x w= 224
Distribute the w to get 2w^2 + 12w= 224
Now divide every number by 2 to get> w^2 + 6w = 112
Now subtrct 112 from both sides to get> w^2 + 6w -112 = 0
Now Factor (w -8)(w+14)=0
w-8=0 >w=8 or w +14=0> w= -14
the width is either 8 or -14 however the width cannot be negative so w=8
subsitute to find L
L= 2w +12
L=2(8)+ 12
L=28

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