Let side lengths of a triangle be #a#, #b#, and #c#. Then how do you proof that #a^2<2(b^2+c^2)#?
1 Answer
Dec 19, 2015
We will use two facts:

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).

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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