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Question

In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.

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Solution

Let the length= l and breadth= b

According to the question-

Area of rectangle -

(l+3)(b4)=lb67 [ Area of rectangle =l×b]
lb4l+3b12=lb67
4l+3b=55
it can also be written as
4l3b=55 ---(1)
Again according to the question-

Area of rectangle

(l1)(b+4)=lb+89
lb+4lb4=lb+89
4lb=93(2)
subtracting (2 )from (1)-

4l4l3b+b=5593
2b=38
b=19
putting this value in equation (1), we get

4l3(19)=55
4l57=55
4l=112
l=28
Hence, length =28 m breadth =19 m


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