Question 252398
We have a right triangle with three sides: AC, BC, and AC. We know that AC = 3X, BC = 5X. If you drew this out, you would see that we are missing side AB. Let this side = KX, where K and X >= 1. 
We apply the pythagorean theorem:
{{{(3x)^2 + (kx)^2 = (5x)^2}}}
this gives us
{{{9x^2 + k^2x^2 + 25x^2}}}
divide out the X^2.
{{{9 + K^2 = 25}}}
solve for K.
K^2 = 16
K = 4.
So, we are dealing with a 3x, 4x, 5x triangle. We need find to x knowing the perimeter = 84. We have
3x + 4x + 5X = 84
12x = 84
x = 7.