Question

the sum of the lenths of any two sides of a triangle must be greater than the third side. if a triangle has one side that is 17 cm and a second side that is 4cm less than twice the third side, what are the possible lenths for the second and third side?

Answer 1

You succinctly state the property being used. Then you give the two sides. What keeps you from figuring the answer?

Using a,b,c for the sides,
a = 17
b = 2c-4

We know that a+b > c, so 17+2c-4 > c
13 > c

So, any value of c < 13 will work.
For example:
a = 17
c = 10
b = 16