SOLUTION: a rectangle is three times as long as it is wide . if its length and width are both decresed by 2cm its area is decreased by 36 cm squared . find its original dimensions

Question 175196: a rectangle is three times as long as it is wide . if its length and width are both decresed by 2cm its area is decreased by 36 cm squared . find its original dimensions
Answer by KnightOwlTutor(293) (Show Source): You can put this solution on YOUR website!
We know that the difference between the 2 areas is 36. Therefore we are going to set up the equation of subtracting the two areas to get the original dimensions.
x=width of the original rectangle
3x=the length of the original rectangle
x-2=width of the smaller rectangle
3x-2=length of the smaller rectangle

the area of a rectangle is width X length
Area of the original rectangle-Area of smaller rectangle=36
(3x*x)-[(x-2)(3x-2)]=36
Use the foil method
3x^2-2x-6x+4
(3x*x)-[3x^2-2x-6x+4]=36
multply -1 to each term contained within the bracket.
Make sure to pay attention to the sign.
(+)(-)=(-)
(-)(-)=(+)
(3x^2-3x^2+2x+6x-4=36
Combine like terms and simplify
(2+6)x-4=36
8x-4=36
Add 4 to both sides of the equation
8x=40
divide both sides by 8
x=5
The dimensions of the original rectangle was 5,15
Let us double check our answer

the dimensions of the smaller rectangle is 3,13
(3*15)-(3*13)=36 75-39=36

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