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

Given:

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

Point U lies on AB and V lies on AC.

UV is perpendicular to AC.

 

Therefore, the similar triangles are AUV and ABC

So the similarity is: segment AU / segment UV = segment AB / segment BC

 

20x + 108       20X + 381
---------       = ---------------
372                      589

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

11780 X + 63612 = 7440X + 141732


4340 X - 78120 = 0


4340 X = 78120

X = 78120/4340 = 18


Answer: x = 18

 

To check:

 

AU = 20*18 + 108 = 360 + 108 = 468

AB = 741

468/372 = 741/589

Which the two are equal ratios