Question

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 the breadth by 2 units the area increase by 67 square units. find the dimensions of the rectangle.

Answer 1

Area of rect. =l*b
lb-9=(l-5)(b+3)
lb-9=lb+3l-5b-15
ie -3l+5b+6

lb+67=(l+3)(b+2)
ie -2l-3b+61

On equating
We will get l=17 and b=9

Answer 2

Heya !!

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Let the length of the rectangle be 'x' units and breadth be 'y' units.

Area = xy sq. units

If length is reduced by 5 units and breadth is increased by 3 units, then area is reduced by 9 sq. units.

xy - 9 = (x-5)(y+3)

=> xy - 9 = xy + 3x - 5y - 15

=> 3x - 5y = 6 _(1)

When length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.

xy + 67 = (x+3)(y+2)

=> xy + 67 = xy + 2x + 3y + 6

=> 2x + 3y = 61 _(2)

Solving _(1) and _(2)

x/(305+18) = y/(-183+12) = 1/(9+10)

=> x = 323/19 = 17

=> y = 171/19 = 9

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

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Hope my ans.'s satisfactory.☺