FILE No.98Unsolved
A carpenter is checking sticks found at a scene. He wants to know which sets of three sticks, joined end to end, make a triangle. Lengths are in inches.
A triangle can be made only when the two shorter sides together are longer than the longest side.
Which set can form a triangle?
If you get stuck, open the hints one at a time, in order.
How must two sides compare with the third?
Focus on the longest side.
Compare it with the sum of the two shorter sides.
Which set can form a triangle?
Choose the answer closest to the truth.
5, 6, 10
The answer is: 5, 6, 10.
Check that two sides always add up to more than the third. For 5, 6, 10: 5 + 6 = 11 > 10, 5 + 10 > 6 and 6 + 10 > 5, so it works.
3, 4, 8: 3 + 4 = 7 is less than 8. 2, 2, 5: 2 + 2 = 4 is less than 5. 1, 2, 3: 1 + 2 = 3 is exactly equal, so the sticks lie flat in a line and do not form a triangle.
People think "exactly equal" just barely works.
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