Question

The length of the rectangle exceeds its breadth by 3 cm. if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. find the length and breadth of the given rectangle.

Answer 1

Let's suppose the breadth of the rectangle be x cm

The length of the rectangle = x + 3 cm

It is assumed that the length and breadth of the rectangle is amplified by 2.

Now, the breadth of the rectangle = x + 2

The length of the rectangle = x + 3 + 2 = x + 5

It is also assumed that the area of the rectangle is 70 sq. cm

Hence, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70

= x2 + 5x + 2x + 10 = 70

= x2 + 7x = 70 - 10

= x2 + 7x = 60

= x2 + 7x - 60 = 0

= x2 + 12x - 5x - 60 = 0

= x( x + 12) -5(x + 12) = 0

= ( x + 12) (x - 5) = 0

=x + 12 = 10 or =x - 5 = 0

= x = 10 - 12 = -2 = x = 5

The breadth of a rectangle is never negative, so the value of x is 5 cm

Therefore, the breadth of the rectangle = 5 cm

The length of the rectangle = 5 + 3 = 8 cm