A owner of a land has 3000m of fencing with which he wishes to enclose a area of rectangular piece of grazing land along a straight portion of a river. Fencing is not required along the river. What could be the possible values of the breadth of the rectangular piece of grazing land if its length is along the river.

Let x denote the breadth of the rectangular piece and y denote the length of the rectangular piece of land.now according to the question

since the total fencing available is 3000 m ,therefore

2x + y = 3000or y = 3000 – 2xand the area (A) = xy

therefore A = x (3000 – 2x)

now if we have to enclose certain area then it has to be greater than zero.

Now , x >0 , y > 0 i.e. 3000 – 2x > 0

Which means that 3000 > 2xOr 2x < 3000Or x < 1500

But length should be greater than the breadth i.e. y>x

Which means that 3000 – 2x > x

Or 3000 > 3x ; x < 1000

Now if we see the three bold solution i.e. x < 1000 , x < 1500 and x >0 then on number line we can plot the result as

hence the value of x lies between 0 and 1000or 0 < x < 1000