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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