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?
The fence with compound wall are forming a right triangle with hypothenuse of 100 m. It can be easily prooved that the maximum area would be with two equal legs, thus the length of each of them is 100/√2. We can write the square of such triangle as 1/2*(cathetus-length)2 = 1/2 (100/√2)2 = 10,000 m2