Question

2) If the length of a rectangle is reduced by 3 cms and breadth increased by 2 cms, it’s area remains same. But if the length is increased by 2 cms and breadth reduced by 1 cm, then too the area remains same. Find the length and the breadth of the rectangle.

Answer 1

Examplular Answer:-

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

=54cmsquare

Hence proved//