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Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.

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TaeKwonDoIsDead

Answer:

[tex]x=8[/tex]


Step-by-step explanation:

In similar triangles, corresponding sides' ratio are equal.

  • Side AB corresponds to Side XY
  • Side BC corresponds to Side YZ
  • Side CA corresponds to Side ZX

We can set up a ratio of [tex]\frac{SideAB}{Side XY}=\frac{SideCA}{Side ZX}[/tex]

Hence, we can write (and solve):

[tex]\frac{Side AB}{Side XY}=\frac{Side CA}{SideZX}\\\frac{2}{4}=\frac{x+7}{4x-2}\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=\frac{32}{4}=8[/tex]

So, x = 8

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