Question

Area of a hall is 288m^2.if length is increased by 6m and breadth decreased by 4m,the area would be unaltered, find the length of the room

Answer 1

Let the initial length and breadth of the rectangle be l and b respectively.
Area = 288 m2
lb = 288 …(i)
When length is increased by 6m and breadth is decreased by 4m ,
Area = 288
(l + 6)(b – 4) = 288
lb – 24 + 6b – 4l = 288 (lb = 288)
6b – 4l = 24
3b – 2l = 12
So, l = (3b – 12)/2 …….(ii)
On putting the value of l in eqn.(i) ,we get
b(3b – 12)/2 = 288
3b2 – 12b – 576 = 0
b2 – 4b – 192 = 0
(b – 16)(b + 12) = 0
So, b = 16 and l = 18
So, length = 18 m.