Question 175196
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