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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= bAccording to the question-Area of rectangle - (l+3)(b−4)=lb−67 [∵ Area of rectangle =l×b] ⇒lb−4l+3b−12=lb−67 ⇒−4l+3b=−55 it can also be written as ⇒4l−3b=55 ---(1) Again according to the question-Area of rectangle (l−1)(b+4)=lb+89 ⇒lb+4l−b−4=lb+89 ⇒4l−b=93−−−(2) subtracting (2 )from (1)- 4l−4l−3b+b=55−93 ⇒−2b=−38 ⇒b=19 putting this value in equation (1), we get 4l−3(19)=55 ⇒4l−57=55 ⇒4l=112 ⇒l=28 Hence, length =28 m breadth =19 m

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