If a + b > c, then, $a^{2} + b^{2} > c^{2}$ for any numbers a,b,c. State true or false.

True

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False

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Solution

The correct option is B False
The statement is false. Consider the triangle with sides 3, 4 and 5.
$3 + 4 > 5$
but $3^{2} + 4^{2} = 5^{2}$

Generally, for any right triangle, the hypotenuse is less than the sum of other two sides (triangle inequality) and the square of the hypotenuse is the sum of the squares of the other two sides (Pythagoras Theorem)

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