The length of a rectangle exceeds its breadth by 4 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 `c m^2` more than that of the given rectangle. Find the length and breadth of the given rectangle.

Explanation

Given:
The length of a rectangle exceeds its breadth by `4 cm`.
If length and breadth are each increased by `3 cm`, the area of the new rectangle will be `81 cm^2 `more than that of the given rectangle.
Let the breadth of the rectangle be `x cm`, then the length will be `(x+4) cm`.
Area of the rectangle`=`length`xx`breadth
Area of rectnagle`=x(x+4)`
Area of rectangle`=(x^2+4x)cm^2`
If both the length and breadth is increased by `3 cm` then,
New length of the triangle will be `(x+4)+3 cm=(x+7) cm`
New breadth of the triangle will be `(x+3) cm`
New area of the triangle`=(x+7)(x+3)`
New area of the triangle`=(x^2+10x+21) cm^2`
According to the question,
New area`=81 cm^2+`Area of the given traingle
`(x^2+10x+21)=(x^2+4x)+81`
`x^2-x^2+10x-4x=81-21`
`6x=60`
`x=60/6`
`x=10 cm`
The length of the triangle will be `(x+4)=10+4=14 cm`.
The breadth of the triangle will be `x=10 cm`.
Hence, the length of the triangle is `14 cm` and breadth of the triangle is `10 cm`.