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Question

The area of a rectangle gets reduced by 67 square metres, when its length is increased by 3 m and breadth is decreased by 4 m.
If the length is reduced by 1 m and breadth is increased by 4 m, the area is increased by 89 square metres. Find the dimensions of the rectangle.

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Solution

Let the length and breadth of the rectangle be x m and y m respectively.
Case1: When length is increased by 3 m and breadth is decreased by 4 m
xy-x+3y-4=67xy-xy+4x-3y+12=674x-3y=55 .....i
Case2: When length is reduced by 1 m and breadth is increased by 4 m
x-1y+4-xy=89xy+4x-y-4-xy=894x-y=93 .....ii
Subtracting (i) from (ii), we get
2y=38y=19
Now, putting y = 19 in (ii), we have
4x-19=934x=93+19=112x=28
Hence, length = 28 m and breadth = 19 m.

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