Since triangle or trigon has three sides, let:
a = side 1
b = side 2
c = side 3
If a and b are the two sides, then, to form a triangle the third side must satisfy the condition:
(a - b ) < c < a + b
Side c must be greater than the difference of sides a and b, but less than the sum of a and b.
Given:
Option 1:
Side a = 3 cm
Side b = 10 cm
Side c = 15 cm
(10-3) < 15 < (3+ 10)
7 < 15 < 13 ⇒ False
⇒ The third side must be
{8, 9, 10, 11, 12},
not {15}
Option 2:
Side a = 10 cm
Side b = 15 cm
Side c = 3 cm
(15-10) < 3 < (10 + 15)
5 < 3 < 25 ⇒ False
⇒ The third side must be
{6, 7, 8, 9, 10, ..., 23, 24, 25},
not {3}
Option 3:
Side a = 15 cm
Side b = 3 cm
Side c = 10 cm
(15-3) < 10 < (15 + 3)
12 < 10 < 18 ⇒ False
⇒ The third side must be
{13, 14, 15, 16, 17}
not {10}
