Question

Please anyone solve this question
The length of a rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of new rectangle will be 84cm ^2 more than original rectangle. Find the length and breadth of the original rectangle.

Answer 1

Let the breadth of the rectangle is x cm.

Given that length of a rectangle exceeds its breadth by 9 cm.

Thus, the length of the rectangle = x + 9 cm.

So, the original dimensions are x and x + 9.

-----------------------------------------------------------------------------------------------------------------

Given that length and breadth increased by 3 cm.

length = x + 3.

Breadth = x + 12.

So, the new dimensions are x + 3 and x + 12

----------------------------------------------------------------------------------------------------------------

Given that Area of new rectangle will be 84cm^2 more than original rectangle.

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

= > x^2 + 9x + 84 = x^2 + 12x + 3x + 36

= > x^2 + 9x + 84 = x^2 + 15x + 36

= > 9x + 84 = 15x + 36

= > x = 8.

So,

Breadth of the original rectangle = 8 cm.

Length of the original rectangle = 17 cm.

Hope this helps!