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Question

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

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Solution

Let breadth of the rectangle = x cm Then length =(x + 9)cm

Area = length × breadth =x(x+9)cm2 By increasing each length and breadth by 3 cm

The new length of the rectangle = x + 9 + 3 = (x + 12) cm and breadth = (x + 3) cm

Area = (x + 12)(x + 3)

According to the condition :

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

6x=8436=48x=486=8

Length of the rectangle = x + 9 = 8 + 9 = 17 cm and breadth = x = 8 cm.


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