SOLUTION: i don't understand how to do this: please help: its a worksheet a rectangle is 12 cm longer than it is wide. if its length and width are both decreased by 2 cm its area is decreas

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i don't understand how to do this: please help: its a worksheet a rectangle is 12 cm longer than it is wide. if its length and width are both decreased by 2 cm its area is decreas      Log On


   

Question 179488: i don't understand how to do this: please help: its a worksheet
a rectangle is 12 cm longer than it is wide. if its length and width are both decreased by 2 cm its area is decreased by 108 cm. squared. find its original dementions.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a rectangle is 12 cm longer than it is wide. if its length and width are both decreased by 2 cm its area is decreased by 108 cm. squared. find its original dimensions.
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Let the width be "x" cm.
Then the length is "x+12" cm
And the area = x(x+12) = x^2+12x cm^2
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Change the dimensions:
width = "x-2" cm
length = "x+10" cm
New area = (x-2)(x+10) = x^2 + 8x - 20 cm^2
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Equations :
Old area - New area = 108 cm^2
x^2+12x -(x^2 + 8x - 20) = 108
4x + 20 = 108
4x = 88
x = 22 cm (original width)
x+12 = 24 cm (original length)
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=original length, W=original width, and A=original area of the rectangle


"a rectangle is 12 cm longer than it is wide." translates to L=W%2B12

and

"if its length and width are both decreased by 2 cm its area is decreased by 108 cm" means that the new area is A-108=%28L-2%29%28W-2%29


Note: the original area of the rectangle is A=LW


A-108=%28L-2%29%28W-2%29 Start with the second equation.


LW-108=%28L-2%29%28W-2%29 Plug in A=LW


%28W%2B12%29W-108=%28W%2B12-2%29%28W-2%29 Plug in L=W%2B12


W%28W%2B12%29-108=%28W%2B12-2%29%28W-2%29 Rearrange the terms.


W%28W%2B12%29-108=%28W%2B10%29%28W-2%29 Combine like terms.


W%28W%2B12%29-108=W%5E2%2B8W-20 FOIL


W%5E2%2B12W-108=W%5E2%2B8W-20 Distribute


4W=88 Subtract W%5E2 from both sides. Subtract 8W from both sides. Add 108 to both sides.


W=88%2F4 Divide both sides by 4 to isolate W.


W=22 Divide. So the original width of the rectangle is 22 cm



L=W%2B12 Go back to the first equation


L=22%2B12 Plug in W=22


L=34 Add. So the original length of the rectangle is 34 cm



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Answer:


So the original dimensions of the rectangle are:

Length: 34 cm
Width: 22 cm