A triangle has two sides of length 1 and 18. What is the smallest possible whole-number length for the third side?

Answer: c must be 18

Explanation:

From the triangle inequality we know that the sum of any two sides must be larger than the third side. We us the inequality here:

a = 1, b = 18, c unknown

a + c > b - > 1 + c > 18 - > c > 17

b + c > a - > 18 + c > 1 - > c > 0

a + b > c - > 18 + 1 > c - > c < 19

The third side must be greater than 17 and smaller than 19. So the smallest possible (and the only possible) whole-number length for c is 18