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There is a square field of side 500 m long each. It has a compound wall along its perimeter. At one of its corners, a triangular area of the field is to be cordoned off by erecting a straight-line fence. The compound wall and the fence will form its borders. If the length of the fence is 100 m, what is the maximum area that can be cordoned off?

1. 2,500 sq m
2. 10,000 sq m
3. 5,000 sq m
4. 20,000 sq m

The Length of the fence(100 m) would be the hypotenuse of the right triangular area which is cordoned.You should also realize that this triangular area would be an isosceles triangle.

Thus,by pythagoras theorem the legs of the right angled isosceles triangle would be :

$100^{2}$ =2$x^{2}$

$x^{2}$=5000

$x=50\sqrt 2$

Area of the triangles would be given by = $50\sqrt 2$ *$50\sqrt 2$=2500 sq m

Hence,Option (A)2500 sq m is the correct choice.