Question

the length of a rectangle is 5cm less than twice its breadth.if the length is decreased by 3cm and breadth increased by 2cm, the perimeter of the resulting rectangle is72 cm. find the area of the original rectangle.
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Answer 1

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Answer 2

Let the breadth of the original rectangle be xcm

Then , length of the original rectangle will be (2x−5)cm

If the length is decreased by 3cm , then ,

New length ={(2x−5)−3}

=(2x−8)cm

If breadth is increased by 2cm , then ,

New breadth =(x+2)cm

New perimeter =2 (new length + new breadth)

=2{(2x−8)+(x+2)}

=2(2x−8+x+2)

=2(3x−6)

We get ,

=6x−12

According to the given problem ,

6x−12=72

6x=72+12

6x=84

x=

6

84

We get ,

x=14

Breadth of the original rectangle =14 cm and

Length of the original rectangle =(2x−5)

=2×14−5

=28−5

=23cm

Area of original rectangle = Length × Breadth

=(23×14)cm

2

=322cm

2

Therefore , area of the original rectangle is 322cm

2