The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm. the area of the new rectangle will be 84 `c m^2` more than that of the given rectangle. Find the length and breadth of the given rectangle.

Explanation

Let the breadth of the rectangle be `x` cm.
The length of the rectangle `=(x+9)` cm.
Area of rectangle`=`length`times`beadth`=x(x+9)cm^2`
Now,
Length of new rectangle`=(x+9+3) cm=(x+12)` cm
Breadth of new rectangle`=(x+3)` cm.
The area of new rectangle`=`length`times`breadth`=(x+12)(x+3)cm^2`
According to the given question:
`(x+12)(x+3)=x(x+9)+84`
`x^2+12x+3x+36=x^2+9x+84`
`15x+36=9x+84`
`15x−9x=84−36`
`6x=48`
`x=8`
`therefore` The breadth of the rectangle `=8` cm
The length of the rectangle`=8+9=17` cm.