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To Be or Not to Be


Determine if the following groups can represent the side lengths of a triangle. If yes, then describe the triangle. If not, then explain why.

{4,4,4}
{4,4,6}
{4,4,8}
{4,4,10}

In order to create a triangle, what must be the relationship between the side lengths? Explain your reasoning.



 Extensions

The integers 2 through 7 are placed into a hat. If three integers are randomly selected without replacement, then what is the probability that they can form the sides of a triangle? How would the results change if the integers were randomly chosen with replacement?



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