QuestionAugust 27, 2025

Which of the following sets of numbers could not represent the three sides of a triangle? Answer 14,16,28 4,16,21 6,11,16 8,20,27

Which of the following sets of numbers could not represent the three sides of a triangle? Answer 14,16,28 4,16,21 6,11,16 8,20,27
Which of the following sets of numbers could not represent the three sides of a triangle?
Answer
 14,16,28 
 4,16,21 
 6,11,16 
 8,20,27

Solution
4.6(161 votes)

Answer

\{ 4,16,21\} Explanation 1. Apply Triangle Inequality Theorem For a set of numbers to represent the sides of a triangle, the sum of any two sides must be greater than the third side. Check each set. 2. Check Set \{ 14,16,28\} 14 + 16 = 30 > 28, 14 + 28 = 42 > 16, 16 + 28 = 44 > 14. This set satisfies the theorem. 3. Check Set \{ 4,16,21\} 4 + 16 = 20 16, 6 + 16 = 22 > 11, 11 + 16 = 27 > 6. This set satisfies the theorem. 5. Check Set \{ 8,20,27\} 8 + 20 = 28 > 27, 8 + 27 = 35 > 20, 20 + 27 = 47 > 8. This set satisfies the theorem.

Explanation

1. Apply Triangle Inequality Theorem<br /> For a set of numbers to represent the sides of a triangle, the sum of any two sides must be greater than the third side. Check each set.<br /><br />2. Check Set $\{ 14,16,28\}$<br /> $14 + 16 = 30 > 28$, $14 + 28 = 42 > 16$, $16 + 28 = 44 > 14$. This set satisfies the theorem.<br /><br />3. Check Set $\{ 4,16,21\}$<br /> $4 + 16 = 20 < 21$. This set does not satisfy the theorem.<br /><br />4. Check Set $\{ 6,11,16\}$<br /> $6 + 11 = 17 > 16$, $6 + 16 = 22 > 11$, $11 + 16 = 27 > 6$. This set satisfies the theorem.<br /><br />5. Check Set $\{ 8,20,27\}$<br /> $8 + 20 = 28 > 27$, $8 + 27 = 35 > 20$, $20 + 27 = 47 > 8$. This set satisfies the theorem.
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