A triangle has integral sides with lengths 4,11, and x. The smallest value x can be is_____?
An obtuse triangle has integer sides of 6,x, and 11. The largest integral value of x is_____?
Can someone please explain these to me.
1) Any two sides of a triangle must add up to more than the third side so x can be as small as we want as long as 4+x>11 x can be integers only so the smallest value of x is x=8
2) Same rule applies on this one. 6+11 > x ---> greatest value of x is 16 Some of these problems require the use of the fact that for an obtuse triangle, a^2 + b^2 < c^2 - but not here (in fact... it might be that only acute triangle problems require that... but it's a^2 + b^2 > c^2 for acute triangles)
