Question 178014: Is it possible for a leg of a right triangle to be longer than its hypotenuse? If it is, when does this occur? IF it is not, why not?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Is it possible for a leg of a right triangle to be longer than its hypotenuse? If it is, when does this occur? IF it is not, why not?
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Impossible.
Assume leg b is greater than hypotenuse c.
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Pythagoras says c^2 = a^2 + b^2
Therefore a^2 = c^2 - b^2
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But if b > c then b^2 > c^2, and a^2 would be negative.
If a is a Real Number a^2 cannot be negative.
Therefore both a < c and b < c
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Cheers,
Stan H.
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