jmc

Question

A stick 5 cm long, a stick 9 cm long, and a third stick n cm long form a triangle. What is the sum of all possible whole number values of n?

Accepted Answer

Using the Triangle Inequality, we see that n > 4 and n < 14, so n can be any integer from 5 to 13, inclusive. The sum can be calculated in several ways, but regardless, 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 81.