# The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres. The area remains unaffected if the length is decreased by 7 metres and breadth is increased by 5 metres. Find the dimensions of the rectangle.

Given:

The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres. The area remains unaffected if the length is decreased by 7 metres and breadth is increased by 5 metres.

To do:

We have to find the dimensions of the rectangle.

Solution:

Let the original length of the rectangle be $l$ and the breadth be $b$.

Area of the original rectangle $=lb$.

In the first case, the length is increased by 7 metres and the breadth is decreased by 3 metres.

New length $=l+7$ m

New breadth $=b-3$ m

The area formed by the new rectangle $=(l+7)(b-3)\ m^2$

According to the question,

$(l+7)(b-3)=lb$

$lb-3l+7b-21=lb$

$3l-7b=-21$.....(i)

In the second case, the length is decreased by 7 metres and breadth is increased by 5 metres.

New length $=l-7$ m

New breadth $=b+5$ m

The area formed by the new rectangle $=(l-7)(b+5)\ m^2$

According to the question,

$(l-7)(b+5)=lb$

$lb+5l-7b-35=lb$

$5l-7b=35$.....(ii)

Subtracting (i) from (ii), we get,

$5l-7b-(3l-7b)=35-(-21)$

$5l-3l-7b+7b=56$

$2l=56$

$l=28$ m

$3(28)-7b=-21$    (From (i))

$84+21=7b$

$b=\frac{105}{7}$

$b=15$ m

The dimensions of the rectangle are $28$ m (length) and $15$ m (breadth).

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Updated on: 10-Oct-2022

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