Expert: Abe Mantell - 7/21/2009

Question
Given two positive constants a and b.

If two sides of a triangle are of length a and b,
find the length of the third side of the triangle in terms of a and b, that maximizes the
area of the triangle.

Thank you


Answer
Since the area of a triangle can be written as:
A=(1/2)(a)(b)sin(C), where C is the angle between the two sides.

So, the maximum area will be when sin(C) is as large as possible.
Thus, C=90 degrees so that sin(C)=1...thus the 3rd side will be
the hypotenuse of the right triangle with legs a and b...
(a^2 + b^2)^(1/2)

Abe