Let side lengths of a triangle be aa, bb, and cc. Then how do you proof that a^2<2(b^2+c^2)a2<2(b2+c2)?
1 Answer
Dec 19, 2015
We will use two facts:
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The sum of lengths of two sides of a triangle is greater than the length of the third side (this is known as the triangle inequality).
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For
b, c in RR ,b^2 + c^2 >= 2bc
As a short justification for (2):
Claim: For a triangle with side lengths
Proof of Claim:
By (1),
As
But by (2),
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