Alg3.1.17

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The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by  3 units.If we increase the length by 3 units  and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.

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

Given that

$(x-5)(y+3)=xy-9\,$

$xy+3x-5y-15=xy-9,3x-5y=6\,$

The other condition is

$(x+3)(y+2)=xy+67\,$

$xy+2x+3y+6=67+xy,2x+3y=61\,$

Solving the two,

$2(3x-5y-6)-3(2x+3y-61)=0,-10y-12-9y+183=0,-19y+171=0,-19y=171,y=9\,$

The value of x is

$3x-5(9)=6,3x=51,x=17\,$

Therefore, the length and breadth of the rectangle are 17 and 9 units respectively.

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