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
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 3rd 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.
Edited on October 27, 2014, 5:25 am