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show that a right triangle of a given hypotenuse has maximum area when it is an isosceles triangle?
The area of a triangle is the half the base times the height. Make the base equal to hypotenuse. To maximize the area, the height must be maximized. The distance from the base to the vertex angle is the greatest when both legs are the same length. Therefore, the largest possible area of a right triangle is possible if it is a isosceles right triangle, when the height is half the length of the base hypotenuse.


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