Geometry math question no guessing and show work you

TRiangles ABC and AUV are similar so their corresponding sides are in the same proportion.

Therefore AU / AB = AV / AC

AB = AU + UB = = 20x + 108 + 273

= 20x + 381

So 20x + 108 / 20x + 381 = 372 / 589

Cross multiply:-

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

11780x + 63612 = 7440x + 141732

4340x = 78120

x = 78120/4340

x = 18 answer

if x = 1, then the answer is 3.5