Question: A rectangular field of a given area is to be fenced off along the bank of a river. no fence is needed along the river,

  1. A rectangular field of a given area is to be fenced off along the bank of a river. no fence is needed along the river, what is the shape of the rectangle requiring the least amount of fencing?
  2. If the hypotenuse of the right triangle is given, show that the area is maximum when the triangle is isosceles.

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