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Question

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

A
Breadth of the rectangle is 13 cm and length =29 cm
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B
Breadth of the rectangle is 5 cm and length =14 cm
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C
Breadth of the rectangle is 3 cm and length =10 cm
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D
Breadth of the rectangle is 8 cm and length =17 cm
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Solution

## The correct option is C Breadth of the rectangle is 8 cm and length =17 cmLet the breadth of the rectangle be x cm. Then, the length of the rectangle is (x+9) cm.So, area of rectangle = length x breadth =x(x+9)cm2Now, length of new rectangle =(x+9+3) cm =(x+12) cm andbreadth of new rectangle =(x+3) cm.So, area of new rectangle = length × breadth =(x+12)(x+3)cm2According to the given condition, (x+12)(x+3)=x(x+9)+84⇒x2+12x+3x+36=x2+9x+84⇒15x+36=9x+84⇒15x−9x=84−36⇒6x=48⇒x=8So, breadth of the rectangle is 8 cm and length =8+9=17 cm.

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