Question 914395: What could represent the side lengths of an obtuse triangle?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The side lengths of an obtuse triangle could be 3, 4 and 6.
With the lengths of the shorter sides being 3 and 4, the length of the longest side in an obtuse triangle must be greater than 5 and less than 7.
A right triangle with legs measuring 3 and 4 has a hypotenuse measuring 5.
To make an obtuse triangle we need a wider angle (one measuring more than 90 degrees).
If the angle between sides with lengths 3 and 4 widens, the third side 's length increases, and becomes greater than 5.
However, the third side of a triangle cannot be equal or greater than the sum of the lengths of the other two sides, and with sides measuring 3 and 4, that sum is 3+4=7.
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