Two sides of an obtuse triangle have lengths 7 and 3. If the third side is also an integer, what are its possible lengths?

Answer 1

If we set a=7 and b=3 then the third side must be c
We need you satisfy the following three conditions when assigning values of c
a+b>c
a+c>b
b+c>a
I will give you two solutions and let you generate the rest...
since we have a=7 and b=3 then from condition 1, a+b>c we know that c can not be bigger than 10 (and since it is an integer answer) the largest thing c can be is 9.
Using condition 1 again let's check 8. If we let c = 8 then condition 2 and 3 are still met
condition 2... a+c>b that is, 7 + 8 > 3
condition ... b + c >a that is 3 + 8 >7
your turn...

Answer 2

PS... this is known as the "Triangle Inequality Theorem "