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

Data:

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

From the figure:

1) Similarity => segment AB / segment BC = segment AU / segment UV

2) segment AB = segment AU + segment UB = 20x + 108 + 273 = 20x + 381

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

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

=> 8880x + 169164 = 14060x + 75924

=> 14060x - 8880x = 169164 - 75924

=> 5180 x = 93240

=> x = 93240 / 5180

=> x = 18

Answer: x = 18