What is the range of possible
lengths of the third side of a
triangle with side lengths of
3 and 7?

4<C <10

Step-by-step explanation:

Theorem: Given a triangle with sides A, B and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

1.  A+B>C

2.  B +C >A

3.  A+C>B

Thus given two sides of A=3 and B=7 C can be:

7 −3<C < 7+3

C range  

4<C <10

step-by-step explanation:

infinity is the answer