SOLUTION: The area of a rectangle is 28 sq inches. The length is 8 more than thrice the width. Find the length and the width.

Question 828560: The area of a rectangle is 28 sq inches. The length is 8 more than thrice the width. Find the length and the width.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
area = L*W
28=(3W+8)(W)
28 = 3W^2+8W
subtract 28 from each side
0 = 3W^2+8W-28
The product of the outer coefficients is 3*(-28) = -84
The product of 14 and -6 is -84 and their sum is 8
so we can solve by parts
3W^2 +14W -6W -28 = 0
W(3W + 14) -2(3W + 14) + 0
(W - 2)(3W + 14) = 0
So W = 2 or W = -14/3
We cannot have a negative length so W = 2
length = (3W+8) = (3*3 + 8 ) = 17
width = 2 and length = 17

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