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 side AB = the side AU + the side UB = 20x + 108 + 273 = 20x + 381

The ratio of side AU to side AV =  the ratio of side AB to side AC

=> AU / AV = AB / AC

=> (20x + 108 ) / 372 = (20x + 381) / 589

Now you can solve for x.

=> 589 * (20x + 108) = 372 * ( 20x + 381)

=> 11780x + 63612 = 7440x + 141732

=> 11780x - 7440x = 141732 - 63612

=>4340x =  78120

=> x = 78120 / 4340

=> x = 18.

x = 18