Alg3.1.18

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If in a rectangle the length is increased and breadth is reduced by 2 units each, the area is reduced by 28 square units.If the length is reduced by 1 unit and breadth is increased by 2 units, the area increases by 33 square units. Find the dimensions of the rectangle.

Let the length and breadth of the rectangle be $x,y\,$ respectively.

As per the first condition

$(x+2)(y-2)=xy-28\,$

$xy-2x+2y-4=xy-28,-2x+2y=-24\,$

$x-y=12\,$

Similarly,the second condition is

$(x-1)(y+2)=xy+33\,$

$xy+2x-y-2=xy+33,2x-y=35\,$

Solving the two equations,

$(x-y-12)-(2x-y-35)=0,x-2x-12+35=0,-x+23=0,x=23\,$

Hence the value of y is

$23-y=12,y=11\,$

Hence the length and breadth of the rectangle are 23 and 11 units respectively.

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