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Pythagorean theorem in 3D

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Each vertical cross-section of the triangular prism shown below is an isosceles triangle.
What is the vertical height, h, of the triangular prism?
Round your answer to the nearest tenth.
The height is
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4