Question

If Z is the incenter of triangle TUV, WZ = 8x - 22 and ZX = 3x +
8, find ZV. Round to the nearest tenth, if necessary.
PLS HELP
GEOMETRY

Answer 1

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Answer:

  ZV ≈ 42.8

Step-by-step explanation:

WZ and ZX and ZY are each radii of the incircle, so are the same length.

  8x -22 = 3x +8

  5x = 30

  x = 6

  ZX = ZY = 3x +8 = 3(6) +8 = 26

ZV is the hypotenuse of right triangle ZVY, which has side lengths of 34 and 26. So, the length of ZV can be found from the Pythagorean theorem as ...

  ZV = √(34² +26²) = √1832

  ZV ≈ 42.8