Question

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.

Answer 1

The answer:
the two triangles are similar
in addition, the line UV is parallel to line BC, so we can use the theorem of Thales for proving the following ratios:

AV /AC = AU/ AB= UV/ BC
372/589=20x +80  / AB = 444 / 703

so we get    (372/589) AB - 80 =  20x, and x = ( (372/589) AB - 80  ) / 20

exact value of x depends on the value of AB