SOLUTION: A right triangle has a fixed hypotenuse of 30 cm. And the other two sides are allowed to vary. Determine the largest possible area of the triangle.

Question 934802: A right triangle has a fixed hypotenuse of 30 cm. And the other two sides are allowed to vary. Determine the largest possible area of the triangle.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= length of one leg, in cm.
= length of the other leg, in cm.
}}}According to the Pythagorean theorem,
<---><--->
The area of the right triangle, in is
,
so

Substituting the expression (found above) for we get
<----><---->
That last expression shows a as quadratic function of ,
and we know that it will have a maximum when <---> .
For that value of ,

and that is the largest possible area of the triangle, in square centimeters.
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