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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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?

Mathematics
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Ahh got it!
BD/AD = AB/AC CD/AD = AC/AB (inverse of above) so BD/AD = AD/CD
BD*CD=AD^2 Now can you do it?

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Other answers:

@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
Solve the equation...
Nice @Callisto, but does my way work?
Oh, sorry forgot this is a new thread
It works too :)
Did you know this can be used to prove Pythagoras' Theorem?
Not sure, the first time I saw this method was in a circle problem. Someone taught me this property... :|
Hey @Sunshine447! Here's how to do it!

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