Question 436465
{{{(x+4)^2 + (x+7)^2 = 9x^2}}}
<==> {{{x^2 + 8x + 16 + x^2 + 14x + 49 = 9x^2}}}
<==>  {{{0 = 7x^2 - 22x - 65 = 0}}}
(x-5)(7x +13) = 0
==> x = 5, -13/7.
Choose only 5.

The sides of the triangle are 9, 12, and 15.
The perimeter is 36 units.