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

Posted by Ady TZIDON on 2014-10-26 04:29:02