The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units . if we increase the length by 10 units and decrease the breadth by 5 units the area increased by 50 sq units . Find the length and breadth of the rectangle.
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The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units . if we increase the length by 10 units and decrease the breadth by 5 units the area increased by 50 sq units . Find the length and breadth of the rectangle.
Good question,
Here is your perfect answer!
Let the length be x and breadth be y.
Area = xy,
1st case,
Length reduced by 5 units = (x-5),
Breadth increased by 2 units = (y+2),
New area = xy - 80
=) (x-5)(y+2) = xy - 80
=) xy + 2x - 5y - 10 = xy - 80
=) 2x - 5y = - 80+10
=) 2x - 5y = - 70 - - 1)
2nd case,
Length increased by 10 units = (x+10),
Breadth decreased by 5 units = (y-5),
New area = xy +50
=) (x+10) (y-5) = xy +50
=) xy - 5x +10y - 50 = xy +50
=) - 5x +10y = 50+50
=) - x + 2y = 20 - - 2)
Multiply it by 2,
=) - 2x + 4y = 40 - - 3)
Add eqs 1 & 3)
=) - 5y + 4y = - 70 + 40
=) - y = - 30
=) y = 30 units,
Put its value in eq2)
=) - x + 2*30 = 20
=) - x + 60 = 20
=) x = 60-20
=) x = 40units,
Hence length = 40 units
Breadth = 30 units.