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
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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) (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.
-----------------
Let the width be "x" cm.
Then the length is "x+12" cm
And the area = x(x+12) = x^2+12x cm^2
----------------------------
Change the dimensions:
width = "x-2" cm
length = "x+10" cm
New area = (x-2)(x+10) = x^2 + 8x - 20 cm^2
------------------
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) (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
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
Note: the original area of the rectangle is
Start with the second equation.
Plug in
Plug in
Rearrange the terms.
Combine like terms.
FOIL
Distribute
Subtract from both sides. Subtract from both sides. Add 108 to both sides.
Divide both sides by 4 to isolate W.
Divide. So the original width of the rectangle is 22 cm
Go back to the first equation
Plug in
Add. So the original length of the rectangle is 34 cm
================================================================
Answer:
So the original dimensions of the rectangle are:
Length: 34 cm
Width: 22 cm
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