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Given : Two sides of triangle 11 and 17
To Find : possible integral lengths for the third side of the triangle
Solution:
Two sides of triangle 11 and 17
Let say third side is X
Sum of any two sides of a triangle is greater than third side
X + 11 > 17
X + 17 > 11 ( this is always true as 17 > 11)
11 + 17 > X
X + 11 > 17 ⇒ X > 6
11 + 17 > X ⇒ 28 > X
Combining both
⇒ 6 < X < 28
X is integer
Hence X can have values from 7 , 8 _______ , 26 , 27
There are 21 possible integral length of 3rd side