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2018 Math Kangaroo

Problem 3

Problem 3 · 2018 Math Kangaroo Medium
Geometry & Measurement

In a triangle one side has length 5 and another side has length 2. The length of the third side is an odd whole number. What is the length of the third side?

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Answer: C — 5
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Hint 1 of 2
The third side must be longer than the difference of the other two and shorter than their sum.
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Hint 2 of 2
It has to be more than 5 − 2 = 3 and less than 5 + 2 = 7.
Show solution
Approach: triangle inequality
  1. The third side must be greater than 5 − 2 = 3 and less than 5 + 2 = 7.
  2. So it lies strictly between 3 and 7.
  3. The only odd whole number in that range is 5.
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