Question

The length of a rectangle exceeds its breadth by $9cm$. If length and breadth are each increased by $3cm$, the area of the new rectangle will be $84c{m}^2$ more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

Let the breadth of the rectangle be $xcm$

Then, length of the rectangle will be $(x+9)cm$

$\therefore$ Area of the rectangle $=\text{length}\times \text{breadth}$

$=x(x+9)c{m}^2$

Now, the length and breadth are increased by $3cm$,

New length $=x+9+3=(x+12)cm$
New breadth $=(x+3)cm$

$\therefore$ Area of new rectangle $=(x+12)(x+3)c{m}^2$

According to the question,

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

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

$15x-9x=84-36$

$6x=48$

$x=\frac{48}{6}$

$x=8$

$\therefore$ Length of the rectangle is $(x+9)=(8+9)=17cm$ and breadth of the rectangle is $8cm$.