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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).
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