SOLUTION: The dimensions of a rectangle are such that length is 9 inches more than width. If the length is doubled and the width decreased by 4 in. The are would be increased by 138 in ^. Wh

Algebra ->  Volume -> SOLUTION: The dimensions of a rectangle are such that length is 9 inches more than width. If the length is doubled and the width decreased by 4 in. The are would be increased by 138 in ^. Wh      Log On


   

Question 980216: The dimensions of a rectangle are such that length is 9 inches more than width. If the length is doubled and the width decreased by 4 in. The are would be increased by 138 in ^. What are the length and width of the rectangle
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x=9+y for length with width y.
Area is %289%2By%29%2Ay=A.

New rectangle,
2%289%2By%29%28y%2B4%29=%28A%2B138%29----OBVIOUS MISTAKE MADE HERE.
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Simplify this new rectangle equation.
2%28y%2B9%29%28y%2B4%29=A%2B138
2%28y%5E2%2B13y%2B36%29-A-138=0
2y%5E2%2B26y%2B72-a-138=0
2y%5E2%2B26y-A-66=0
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What to do next, is substitute for A using the original area equation.
2y%5E2%2B26y-%28y%5E2%2B9y%29-66=0
2y%5E2%2B26y-y%5E2-9y-66=0
y%5E2%2B17y-66=0
%28y-6%29%28y%2B11%29=0
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The meaningful value for *y is highlight%28y=6%29.
*x=y%2B9=6%2B9=highlight%2815=x%29.
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*Those are wrong, because of the noted OBVIOUS MISTAKE.
New rectangle width should be y-4, not y+4.


DONE CORRECTLY, THIS IS HOW THE STEPS GO:
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system%28x=y%2B9%2C+y%28y%2B9%29=A%29

NEW: 2%28y%2B9%29%28y-4%29=A%2B138
2%28y%5E2%2B5y-36%29=A%2B138
2y%5E2%2B10y-72-138-A=0
2y%5E2%2B10y-y%5E2-9y-72-138=0
2y%5E2%2B10y-y%5E2-9y-210=0
y%5E2%2By-210=0
%28y-14%29%28y%2B15%29=0
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highlight%28y=14%29
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Returning to x=y%2B9
x=14%2B9
highlight%28x=23%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The dimensions of a rectangle are such that length is 9 inches more than width. If the length is doubled and the width decreased by 4 in. The are would be increased by 138 in ^. What are the length and width of the rectangle
Width of original rectangle: highlight_green%2814%29 in

Length of original rectangle: 14 + 9, or highlight_green%2823%29 im