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}**