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There is a square field with each side 500 metres long. It has a compound wall along its perimeter. At one of its comers, 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 metres, what is the maximum area in square metres that can be cordoned off?
Let EF be the fence.
As the field is in the shape of a square, the straight line face that is put up will cordon a field of the form right angled triangle.
The area of a right angled triangle is maximum when the sides that contain the right angle are equal.
Let the side be a.
$$a^2 + a^2$$ = $$100^2$$ => $$a = 50\sqrt{2}$$
Area = $$\frac{1}{2}*50\sqrt{2}*50\sqrt{2}$$ = 2500 sq m.
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