The breadth of a rectangle is 4 cm less than its length if the length is increased by 4 cm and the breadth is decreased by 1 cm, the area of the rectangle is increased by $40\ cm^2$. Find the length and breadth of the rectangle.

Given:

The breadth of a rectangle is 4 cm less than its length. If the length is increased by 4 cm and the breadth is decreased by 1 cm, the area of the rectangle is increased by $40\ cm^2$.

To do:

We have to find the dimensions of the rectangle.

Solution:

Let the original length of the rectangle be $l$. 

This implies,

The breadth of the rectangle $=l-4\ cm$

Area of the original rectangle $=l(l-4)\ cm^2$.

The length is increased by 4 cm and the breadth is decreased by 1 cm, the area of the rectangle is increased by $40\ cm^2$. 

New length $=l+4$ cm

New breadth $=(l-4)-1=l-5$ cm

The area formed by the new rectangle $=(l+4)(l-5)\ cm^2$

According to the question,

$(l+4)(l-5)=l(l-4)+40$

$l^2-5l+4l-20=l^2-4l+40$

$4l+4l-5l=40+20$

$3l=60$

$l=20\ cm$

$\Rightarrow l-4=20-4=16\ cm$

The dimensions of the rectangle are $20\ cm$ (length) and $16\ cm$ (breadth).