A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum perimeter of the triangle?
+128475 The hypotenuse will lie on the diameter
The perimeter is maximized when the legs are equal....using the Pythagorean Theorem
L^2 + L^2 = 100^2
2L^2 =100^2
L^2 = 100^2/2
L = 100/sqrt 2
So...the max perimeter is 100 + 2 * 100/sqrt 2 = 100 ( 1 + sqrt 2) units ≈ 241.42 units
