SOLUTION: Could 2,3, and 6 represent the lengths of sides of a right triangle? Justify your answer. I hope I made it clear enough for you to understand. Thanks for your help!

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Question 176783: Could 2,3, and 6 represent the lengths of sides of a right triangle? Justify your answer.
I hope I made it clear enough for you to understand.
Thanks for your help!
Found 2 solutions by Mathtut, jojo14344:
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
perfectly clear
:
for a right triangle we know that sum of each side squared= hypothenuse squared
:
so if this is a right triangle this should hold true
:
we know that the longest side is the hypothenuse
:

:

:
since this statement is not true
we can conclude that this is not a right triangle

Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website!

We know a Right triangle is governed by Pythagorean Theorem, where the Square of the hypotenuse is equal to the sum of the squares of the other 2 sides.
Given----> (hypotenuse being the longest)
To show:

Pythagorean theorem states:

,----> Does not satisfy the theorem, therefore the Lengths cannot represent the Sides of a RIGHT TRIANGLE.
Thank you,
Jojo