Question

The length of rectangle is greater than the breadth by 3 cm if the length is increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same.
Find the dimensions of the rectangle.
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Answer 1

Answer:

54 cm

Step-by-step explanation:

Let the breadth of the rectangle be Xcm

Then, the length of the rectangle be (x+3)cm

∴ Area of the rectangle =(x+3)×xcm

2

−−−−−(1)

Given that

Length is increased by 9=x+3+9=x+12cm

and, breadth is reduced by 3=x−3cm

Now,

Area of new rectangle (x+12)×(x−3)cm

2

−−−−−(2)

But in the given question we have given that the both area is same

then we can get

(x+3)×x=(x+12)×(x−3)

⇒x

2

+3x=x

2

+12x−3x−36

⇒6x=36

∴x=6

Now,fromequation(1)

Areaoftherectangle=(x+3)×x

=(6+3)6

=54cm

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