triangles

[popeyesmom]

Please help with his problem on a middle school level. Thank you very much!
Two sides of a nonisosceles triangle measure 6 cm and 11 cm. If the length, in centimeters, of the third side is also an integer, how many possible lengths can the third side be?

 

[pka]

Please help with his problem on a middle school level. Thank you very much!
Two sides of a nonisosceles triangle measure 6 cm and 11 cm. If the length, in centimeters, of the third side is also an integer, how many possible lengths can the third side be?

Use the triangle inequality. Let \(\displaystyle n\) denote the integer of the third side.
That means \(\displaystyle n<6+11,~6<11+n,~\&~11<n+6\).
What integer values satisfy those three?