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Sunshine447

  • 3 years ago

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 16 and 25. What is the length of the altitude?

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  1. apple_pi
    • 3 years ago
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    Ahh got it!

  2. apple_pi
    • 3 years ago
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    BD/AD = AB/AC CD/AD = AC/AB (inverse of above) so BD/AD = AD/CD

  3. apple_pi
    • 3 years ago
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    BD*CD=AD^2 Now can you do it?

  4. apple_pi
    • 3 years ago
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    @Sunshine447

  5. Callisto
    • 3 years ago
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    @apple_pi I would do it in this way |dw:1344514762278:dw| a^2+b^2 = (16+25)^2 a^2 = c^2 + 16^2 -(1) b^2 = c^2 + 25^2 -(2) (1) + (2) a^2 + b^2 = c^2 + 16^2 + c^2 + 25^2 (16+25)^2 = 2c^2 + 16^2 + 25^2

  6. Callisto
    • 3 years ago
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    Solve the equation...

  7. apple_pi
    • 3 years ago
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    Nice @Callisto, but does my way work?

  8. apple_pi
    • 3 years ago
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    Oh, sorry forgot this is a new thread

  9. Callisto
    • 3 years ago
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    It works too :)

  10. apple_pi
    • 3 years ago
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    Did you know this can be used to prove Pythagoras' Theorem?

  11. Callisto
    • 3 years ago
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    Not sure, the first time I saw this method was in a circle problem. Someone taught me this property... :|

  12. apple_pi
    • 3 years ago
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    Hey @Sunshine447! Here's how to do it!

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