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.

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Answer 1

The tirangle AUV is inside triangle ABC.

Side AV is on side AC.

Side AU is on side AB.

Side UV is parallel to BC.

Simiilaritiy properties =>

AU/ AV = AB / AC

=> (20x + 108) / 372 = (20x + 108 + 273) / 589

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

=> 11780x + 63612 = 7440x + 141732

=> 11780x - 7440x = 141732 - 63612

=> 4340x = 78120

x = 78120 / 4340 = 18

Answer: 18