Question

The length of a rectangle exceeds its breadth by 5 cm if length
and breadth are each increased by 5 cm, the area of a rectangle will
be 250 sq. Cm more than that of the given rectangle. Find the length
and the breadth of the given rectangle.

Answer 1

Let the breadth of the rectangle be x cm.

Then, the length of the rectangle is (x+9) cm.

So, area of rectangle = length x breadth =x(x+9)cm

2

Now, length of new rectangle =(x+9+3) cm =(x+12) cm and

breadth of new rectangle =(x+3) cm.

So, area of new rectangle = length × breadth =(x+12)(x+3)cm

2

According to the given condition,

(x+12)(x+3)=x(x+9)+84

⇒x

2

+12x+3x+36=x

2

+9x+84

⇒15x+36=9x+84

⇒15x−9x=84−36

⇒6x=48

⇒x=8

So, breadth of the rectangle is 8 cm and length

=8+9=17 cm.

Answer 2

Answer

Let the breadth of the rectangle be x cm. 

Then, the length of the rectangle is (x+9) cm.

So, area of rectangle = length x breadth =x(x+9)cm2

Now, length of new rectangle =(x+9+3) cm =(x+12) cm and

breadth of new rectangle =(x+3) cm.

So, area of new rectangle = length × breadth =(x+12)(x+3)cm2

According to the given condition, 

(x+12)(x+3)=x(x+9)+84

⇒x2+12x+3x+36=x2+9x+84

⇒15x+36=9x+84

⇒15x−9x=84−36

⇒6x=48⇒x=8

So, breadth of the rectangle is 8 cm and length 

=8+9=17 cm.