Question

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm² more than that of the given rectangle. Find the length and breath of the given rectangle.

Answer 1

Let the breadth of the rectangle be x cm . 
Therefore, the length of the rectangle will be (x + 9) cm. 
∴ Area of the rectangle =\[ x(x + 9) {cm}^2. \] 
If the length and breadth are increased by 3 cm each, 
area \[= (x + 3)(x + 9 + 3) {cm}^2. \]
Now, 
\[(x + 3)(x + 12) - x(x + 9) = 84\]
or \[x^2 + 15x + 36 - x^2 - 9x = 84\]
or 6x = 84 - 36
or \[x = \frac{48}{6} = 8 . \]
Thus, breadth of the rectangle = 8 cm. 
Length of the rectangle = (8 + 9) = 17 cm.