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Question

# The area of a rectangle increases by 200m2, if the length is increased by 8 m and the breadth by 3 m. The area increases by 255m2, if the length is increased by 3 m and breadth by 8 m. Find the length and the breadth of the rectangle.

A
l=4 m, b=4 m
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B
l=24 m, b=13 m
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C
l=13 m, b=18 m
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D
l=21 m, b=8 m
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Solution

## The correct option is B l=24 m, b=13 mLet the numbers be x and y:Given, (x+8)(y+3)=200+xy ....(1)and (x+3)(y+8)=255+xy ....(2)Simplifying the 2 equations, we get3x+8y=1763y+8x=231x=(−8y+176)3Substituting this value of x in any equation, we get 3y+8(−8y+176)3=231Thus, x=24 and y=13.Therefore, length is 24 m and breadth =13 m.

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