SOLUTION: A rectangular cutting board is 6 inches longer than it is wide. If the area of the cutting board is 216 square inches, find the length and the width. I figured finding the square r

Algebra ->  Rectangles -> SOLUTION: A rectangular cutting board is 6 inches longer than it is wide. If the area of the cutting board is 216 square inches, find the length and the width. I figured finding the square r      Log On


   

Question 314897: A rectangular cutting board is 6 inches longer than it is wide. If the area of the cutting board is 216 square inches, find the length and the width. I figured finding the square root would help a bit, sqrt or 216 is about 14.7, i tried to subtract 6 then add six and i just made myself confused.
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"A rectangular cutting board is 6 inches longer than it is wide. If the area of the cutting board is 216 square inches, find the length and the width. I figured finding the square root would help a bit, sqrt or 216 is about 14.7, i tried to subtract 6 then add six and i just made myself confused."
area of a rectangle A = length L * width W
A = (W + 6) * W = 216 (length is 6 inches longer than width)
A = W^2 + 6W = 216
W^2 + 6W - 216 = 0 (solve for W, throw out negative answer)
W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 1, b = 6, c = -216
W+=+%28-6+%2B-+sqrt%28+36+-+4%2A%28-216%29+%29%29%2F2+
W+=+%28-6+%2B-+sqrt%2836+%2B+864%29%29%2F2+
W+=+%28-6+%2B-+sqrt%28900%29%29%2F2+
W+=+%28-6+%2B-+30%29%2F2+
W = (-6 + 30)/2 or W = (-6 - 30)/2
W = 24/2 = 12 or W = -36/2 = -18
W = 12 since W can not be negative
18 * 12 = 216