Bunuel wrote:

Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 9, and 13, what is the value of r?

A. 5

B. 17

C. 18

D. 22

E. 29

Kudos for a correct solution.

Sides of triangle are q, 9 and 13

for a triangle to exist

Sum of the two sides > third sidei.e. For Smallest value of q

q + 9 > 13

i.e. q > 4

i.e. For Largest value of q

13 + 9 > q

i.e. q < 22

i.e. q can be any Integer from 5 to 21

Total Possible values of q = r = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}

i.e. r = 17

Answer: Option B

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