If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.
Given:
If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units.
To do:
We have to find the area 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 and breadth reduced each by 2 units, the area is reduced by 28 square units.
New length $=l+2$
New breadth $=b-2$
The area formed by the new rectangle $=(l+2)(b-2)$
According to the question,
$(l+2)(b-2)=lb-28$
$lb-2l+2b-4=lb-28$
$2l-2b=28-4$
$2(l-b)=24$
$l-b=12$.....(i)
In the second case, the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units.
New length $=l-1$
New breadth $=b+2$
The area formed by the new rectangle $=(l-1)(b+2)$
According to the question,
$(l-1)(b+2)=lb+33$
$lb+2l-b-2=lb+33$
$2l-b=33+2$
$2l-b=35$.....(ii)
Subtracting (i) from (ii), we get,
$2l-b-(l-b)=35-12$
$2l-l-b+b=23$
$l=23$ units
$23-b=12$ (From (i))
$b=23-12$
$b=11$ units
The area of the original rectangle $=lb$
$=23\times11$
$=253$ square units.
The area of the rectangle is $253$ square units.
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