SOLUTION: A book is three times as long as it is wide. Find the length and width of the book if the area is 128 more than the perimeter of the book.

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Question 212028: A book is three times as long as it is wide. Find the length and width of the book if the area is 128 more than the perimeter of the book.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
L=3w
2(L+w)+128=Lw
2(3w+w)+128=3w*w substitute 3w for L
8w+128=3w^2
3w^2-8w-128=0 subtract the left side of the equation from the right.
3*-128=-384 Multiply the 1st and the last coefficients.
What 2 factors of -384 give a sum of -8? Answer: -24 and 16
3w^2-24w+16w-128=0
3w(w-8)+16(w-8)=0
(3w+16)(w-8)=0 Factoring by grouping.
w=8
L=24
.
Ed