Given that the two triangles are similar, solve for x if au = 20x + 108, ub = 273, bc = 703, uv = 444, av = 372 and ac = 589.

The lengths of the sides of the triangles are:

AU = 20x + 108,
UB = 273,
BC = 703,
UV = 444,
AV = 372 and
AC = 589.

Similarity implies: AB / BC = AU / UV

And AB = AU + UV = 20x + 108 + 273 = 20x + 381

=> (20x + 381) / (703) = (20x + 108) / 444

=> (20x + 381) (444) = (20x + 108)(703)

=> 8880x + 169164 = 14060x + 75924

=> 14060x - 8880x = 169164 - 75924

=> 5180x = 93240

=> x = 93240 / 5180

=> x = 18

18