SOLUTION: the length of a rectangle is 1 inch more than 2 times its width. the area of the rectangle is 36 square inches. what is the length of the rectangle?

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Question 297877: the length of a rectangle is 1 inch more than 2 times its width. the area of the rectangle is 36 square inches. what is the length of the rectangle?
Found 2 solutions by JBarnum, Stitch:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
L=(2W+1)
A=LW
A=36
36=LW
36=%282W%2B1%29W
36=2W%5E2%2BW
0=2W%5E2%2BW-36
0=2%28W%5E2%2B0.5W-18%29 -4 and 4.5 are the 2 numbers that multiply to get -18 add to get 0.5
0=2%28W-4%29%28W%2B4.5%29
W=highlight%284%29,cross%28-4.5%29 cant be negative
L=%282W%2B1%29
L=%282%284%29%2B1%29
L=highlight%289%29



Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Set-Up
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Equation 1: L+=+1+%2B+2W
Equation 2: L+%2A+W+=+36
Solution:
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Substitute (1 + 2W) into equation 2 for L
Equation 2: L+%2A+W+=+36
%281+%2B+2W%29+%2A+W+=+36 Simplify
W+%2B+2W%5E2+=+36 Subtract 36 from both sides
W+%2B+2W%5E2+-+36+=+0 Rewrite the equation
2W%5E2+%2B+W+-+36+=+0
Find the factors of 36: 1,2,3,4,6,9,12,18,36
In this case 4 & 9 fit our equation
%282W+%2B+9%29%2A%28W+-+4%29+=+2W%5E2+-+8W+%2B+9W+-+36+=+2W%5E2+%2B+W+-+36
The new equation: %282W+%2B+9%29+%2A+%28W-4%29+=+0
There are 2 answers: (2W + 9 = 0) & (W - 4 = 0)
2W+%2B+9+=+0 Subtract 9 from both sides
2W+=+-9 Divide both sides by 2
W+=+-4.5
Now you can not have a negative length so that rules out that answer
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For W+-+4+=+0 Add 4 to both sides
highlight%28W+=+4%29
Now plug 4 into equation 1 for W
Equation 1: L+=+1+%2B+2W
L+=+1+%2B+2%2A%284%29
highlight%28L+=+9%29