Question

The area of a rectangle gets reduced by 80sq.units .if ots length is reduced by 5 unots and breadth is increased by 2 units .if we increase the length by 10 units and decrease the breadth by 5 units,the area will increase by 50 sq.units .find the length and breadth of the rectangle

Answer 1

Let the length of rectangle be l and breadth be b.
Area of a rectangle = l × b
1st condition : (l-5)(b+2) = (lb-80)
lb + 2l - 5b - 10 = lb - 80
2l - 5b = -70 -------------(1)
2nd condition : (l+10)(b-5) = (lb+50)
lb - 5l + 10b - 50 = lb + 50
-5l + 10b = 100
l - 2b = -20 --------------(2)
multiplying (2) by 2, we get
2l - 4b = -40 -------------(3)
Subtracting (3) from (1)
2l - 5b - 2l + 4b = -70 + 40
-b = -30
b = 30 (put in (2))
l - 2(30) = -20
l = -20 + 60 = 40
So, length = 40 units and breadth = 30 units