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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.
Solution
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.
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