SOLUTION: The length of a rectangle is 5 inches more than twice the width. The area of the rectangle is 102 inches square. How long is the rectangle?

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Question 205643: The length of a rectangle is 5 inches more than twice the width. The area of the rectangle is 102 inches square. How long is the rectangle?
Found 2 solutions by Earlsdon, Targetweek:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) L+=+2W%2B5 "The length (L) of a rectangle is 5 more than twice its width (W)."
2) L%2AW+=+102sq.in. "The area of the rectangle is 102 inches square."
What is L?
Substitute the L from equation 1) into equation 2) and solve for W.
%282W%2B5%29%2AW+=+102
2W%5E2%2B5W+=+102 Subtract 102 from both sides.
2W%5E2%2B5W-102+=+0 Factor this quadratic equation.
%282W%2B17%29%28W-6%29+=+0 Apply the zero product rule.
2W%2B17+=+0 or W-6+=+0 which means that...
2W+=+-17 or W+=+6 Discard the negative solution as the width, W, must be a positive value.
W+=+6inches and...
L+=+2W%2B5
L+=+2%286%29%2B5
highlight%28L+=+17%29inches.

Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
First we'll start with what formula to use
A+=+LW
1. Since the length of a rectangle is 5 inches more than twice the width we can write the following equation
L=2W%2B5
2. Now we have two equations in a system of equations
LW=102 and
L=2W%2B5
3. First substitute the 2nd equation into the 1st
%282W%2B5%29W=102
- then simplify
2W%5E2%2B5W=102
2W%5E2%2B5w-102+=+0
- next factor the equation
%282W%2B17%29%28W-6%29+=+0
- then set each factor equal to 0 and solve for W
2W%2B17+=+0 and W-6+=0
2W=-17 and w=6
W+=+-17%2F2 amd w=6
- Because we can't have a negative side length the only answer is 6
4. So W = 6 and now plug W into the 2nd equation
L+=+2W%2B5
L+=+2%286%29+%2B+5
L+=+12%2B5
L=17
5. So L = 17
The final answer is W = 6, L = 17