vampirewitchreine said:
... from the textbook is "Can the lengths 2, 6, and 5 make a triangle?"
My first thought was to kinda do it like Pythagorean theorem, but I'm unsure if this would be correct.
This is what I got when I did that
2^2*6^2(=?)5^2
4*36(=?)25
40(=\)25
Is this wrong? I just want to know how to do this right so that I know for future reference. Please help.
\(\displaystyle \text{ Please refer to the reply of royhaas regarding your specific question.}\)
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What if instead you're asked if those could be the side lengths of a right triangle. ***
Choose the side length which is longest to be c (the hypotenuse),
because the hypotenuse is always the longest side of a right triangle.
\(\displaystyle a^2 \ + \ b^2 \ = \ c^2\)
\(\displaystyle 2^2 \ + \ 5^2 \ = \ ? \ 6^2\)
\(\displaystyle 4 \ + \ 25 \ = \ ? \ 36\)
\(\displaystyle 29 \ \ne \ 36\)
So, for this different question, it would not be a right triangle.
But you wouldn't bother to use this method if you found out
at first that those sides couldn't even form *any* triangle at all.
\(\displaystyle \text{*** However, if the question were different}\)
\(\displaystyle \text{and had asked if those sides could}\)
\(\displaystyle \text{be those of a right triangle, then yes,}\)
\(\displaystyle \text{you could the Pythagorean Theorem.}\)