Question

The length of a rectangle exceeds its breadth by 3 cm. If each of the length and breadth are increased by 2 cm, the area of the new rectangle will be 58cm² more than the area of the given rectangle. Find the length and breadth of the given rectangle.​

Answer 1

Given :

• Length of the Rectangle is 3 more than the breadth of the Rectangle.

• Increase in length and breadth = 2 cm

• Area of the new Rectangle = 58 cm² more than the area of the orginal Rectangle.

To find :

The orginal length and breadth of the Rectangle.

Solution :

Let the breadth of the Rectangle be x cm , so according to the Question , we get the length of the Rectangle as (x + 3) cm.

By moving further , we get that the length and breadth of the Rectangle is increased by 2 i.e,

• New length = [(x + 3) + 2] cm

• New Breadth = x + 2 cm

We know the formula for area of a Rectangle i.e,

$\boxed{\bf{Area\:(A) = Length\:(L) \times Breadth\:(B)}}$

Now , Substituting the values in the formula byaccording to the Question , we get the Equation as,

$:\implies \bf{[(x + 3) \times x] + 58 = [(x + 3) + 2] \times (x + 2)}$

Now by solving this Equation , we get :

$:\implies \bf{x^{2} + 3x + 58 = (x + 5) \times (x + 2)}$

$:\implies \bf{x^{2} + 3x + 58 = x^{2} + 2x + 5x + 10}$

$:\implies \bf{x^{2} - x^{2} + 58 - 10 = 2x + 5x - 3x}$

$:\implies \bf{\not{x^{2}} - \not{x^{2}} + 58 - 10 = 2x + 5x - 3x}$

$:\implies \bf{58 - 10 = 2x + 5x - 3x}$

$:\implies \bf{48 = 2x + 5x - 3x}$

$:\implies \bf{48 = 4x}$

$:\implies \bf{\dfrac{48}{4} = x}$

$:\implies \bf{12 = x}$

$\boxed{\therefore \bf{x = 12}}$

Hence, the value of x is 12 .

Since, we have taken the breadth of the Rectangle is x , thus the breadth of the Rectangle is 12 cm.

And we have taken the length of the Rectangle as (x + 3) , the Length of the Rectangle is 15 cm.