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Which of the following sets of numbers could not represent the three sides of a triangle?
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Q. Which of the following sets of numbers could not represent the three sides of a triangle?
- Recall Triangle Inequality Theorem: Recall the Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Apply Theorem to First Set: Apply the Triangle Inequality Theorem to the first set of numbers .Check if 9 + 19 > 27. The sum is , which is greater than .Check if 9 + 27 > 19. The sum is , which is greater than .Check if 19 + 27 > 9. The sum is , which is greater than .All conditions are satisfied, so could represent the sides of a triangle.
- Apply Theorem to Second Set: Apply the Triangle Inequality Theorem to the second set of numbers . Check if 6 + 20 > 27. The sum is , which is not greater than . Since this condition is not satisfied, cannot represent the sides of a triangle.
- Conclude Invalid Set: Since we have already found a set of numbers that cannot represent the sides of a triangle, we do not need to check the remaining sets. We can conclude that is the set that cannot represent the sides of a triangle.
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