In triangle ABC, it is known that AB = 9 and BC/AC = 40/41.

Find the maximum possible area of the triangle ABC.

**Nice problem and nice solutions.**

I, too got

Answer**: 820**

I have assumed ABC consisting of 40k, 41k and 9 as its sides and looked for the **k** for which the area is the largest.

The results: k=6.364475 and the sides of ABC are 254.575, 260.9435 and 9.

I assumed that the relation **820 = .5*41*40** is purely incidental, since the 3^{rd} side is not represented in the equation.

Broll's solution and Bractal's comments shed some light on this "too good to be a coincidence" fact and the puzzle got a wider perspective of exploration.

Good work!

*Edited on ***October 27, 2014, 5:25 am**