Is This Right Triangle Impossible?

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There is a story that tells of a geometry problem that was given to a math class. The problem seemed simple, but everyone got it wrong. Here's the math problem: There is a right triangle with a hypotenuse of ten and an altitude to the hypotenuse of six. What is the area of this triangle? This is a trick question, because such a triangle cannot exist. Do you know why the right triangle described in this problem is impossible?

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