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Which inequalities represent the possible lengths for the third side, x?

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3 Answers

let a,b, and c be the lengths of the three sides of a triangle
there are three inequalities:
for your lengths, let a=16 and b=6, therefore a+b>c or 16+6>c; so 22>c or c<22
c can be how much less than 22 ?
look at b+c>a, 6+c>16, c>10
therefore c can be in the following range: 10<c<22
Rule for Δ ABC: any two sides added together must be greater than the third side.
      AB = c
      BC = a
      AC = b,
    a + b > c
    a + c > b
    b + c > a

If one side of triangle is 6 units, second side is 16 units and third one is "x" units then

   x < 16 + 6 
   x < 22

   6 + x > 16
   x > 10

   10 < x < 22
The sum of the lengths of any two sides of a triangle must be greater than the third side. Thus, in your case, any length greater than 16+6 = 22 is a valid length for x.