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The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments whose lengths are in the ratio of 1:4. The length of the altitude is 12. How long is the hypotenuse?

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sqdancefan

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Answer:

  30

Step-by-step explanation:

The altitude is the geometric mean of the two segments of the hypotenuse. For some scale factor x, the segments are 1x and 4x, and the altitude is ...

  12 = √((1x)(4x)) = 2x

  6 = x

So, the length of the hypotenuse is ...

  (1x) +(4x) = 5x = 5·6 = 30

The hypotenuse is 30 units long.

Answer:

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Step-by-step explanation:

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