Two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 44at the4, AV = 372 and AC = 589.

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06-07-2017
Mathematics

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Two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 44at the4, AV = 372 and AC = 589.

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Edufirst Edufirst · Answer 1 · 2017-07-17T13:25:26+02:00

The right information from the figure is:

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

The similarity of the two triangles leads to:

[AB] / [AC] = [AU] / [AV]

[AB] = [AU] + [UB] = 20x + 108 + 273 = 20x + 381

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

Now you can solve for x.

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

=> 7440x + 141732 = 11780x + 63612

=> 11780x - 7440x = 141732 - 63612

=> 4340x = 78120

=> x = 18

Answer: x = 18