Geometry and TrigonometryVery hardCounting possible integer third sides
Geometry and Trigonometry practice question
Two sides of a triangle have lengths 7 and 12. If the third side has an integer length, how many different lengths are possible for the third side?
Answer: 13
The third side must satisfy 12 − 7 < x < 12 + 7, so 5 < x < 19: the integers 6 through 18, which is 13 values.
Common wrong answers
- If you answered 12
- 12 misses one end of the range.
- If you answered 14
- 14 wrongly includes an endpoint; the inequalities are strict.
- If you answered 19
- 19 counts every integer up to the sum.
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