You are given a triangle with side lengths of 3, 7 and x. Use this to answer the following questions. Be sure all answers are exact and in simplest radical form where appropriate. (When the problems refer to the "longest side", there may be another side of the triangle equal to the longest side but not greater.)
a) Write an inequality to represent all possible values for x that will make a triangle. (1 pt)
b) Find the value of x that makes the triangle right when the longest side is 7. (1 pt)
c) Find the value of x that makes the triangle right when x is the longest side of the triangle. (1pt)
d) Find the value(s) of x that will make the triangle acute when the longest side is 7. (1 pt)
e) Find the value(s) of x that will make the triangle acute when the longest side is x. (1 pt)
f) Find the value(s) of x that will make the triangle obtuse when the longest side is 7. (1 pt)
g) Find the value(s) of x that will make the triangle obtuse when the longest side is x. (1 pt)
Describe all values of x that make the triangle right, acute and obtuse with sides of 3, 7 and x. (3 pts)