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.

Mathematics

1 answer:

KatRina [158]3 years ago

5 0

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

$\cfrac{AU}{AB} =\cfrac{UV}{BC} \\ \\ \cfrac{20x+108}{20x+381} =\cfrac{444}{703} \\ \\ 703(20x+108)=444(20x+381)\\\\14060x+75924=8880x+169164 \\ \\ 14060x-8880x = 169164 - 75924 \\ \\ 5180x = 93240 \\ \\ x=93240/5180 \\ \\ x=18$

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