Sunshine447
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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apple_pi
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Ahh got it!
apple_pi
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BD/AD = AB/AC
CD/AD = AC/AB (inverse of above)
so BD/AD = AD/CD
apple_pi
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BD*CD=AD^2
Now can you do it?
apple_pi
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@Sunshine447
Callisto
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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
Callisto
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Solve the equation...
apple_pi
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Nice @Callisto, but does my way work?
apple_pi
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Oh, sorry forgot this is a new thread
Callisto
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It works too :)
apple_pi
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Did you know this can be used to prove Pythagoras' Theorem?
Callisto
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Not sure, the first time I saw this method was in a circle problem. Someone taught me this property... :|
apple_pi
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Hey @Sunshine447! Here's how to do it!