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.Com
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


RELATED QUESTIONS

i don't understand how to do this can you please help me? its a worksheet the problem... (answered by Alan3354,josmiceli)
A rectangle is 12 cm longer than it is wide. Its perimeter is 100 cm. Find its length and (answered by richard1234)
A rectangle is 8 cm longer than it is wide. Find the dimensions of the rectangle if its... (answered by Grinnell,mananth)
A rectangle is 7 times longer than it is wide. If its perimeter is 144 cm, what is its... (answered by Alan3354)
I do not understand how to chart a problem. this is the problem that was given to me:... (answered by ankor@dixie-net.com)
a rectangle is three times as long as it is wide. If its length and width are both... (answered by graphmatics)
A rectangle is 3 cm longer than it is wide. Find the dimensions of the rectangle if its... (answered by josgarithmetic)
a rectangle is 12 meters longer than it is wide. its perimeter is 68 meters. find its... (answered by checkley77)
a rectangle is 12 meters longer than it is wide. its perimeter is 68 meters find its... (answered by mananth)