Which of the following sets of numbers could not represent the three sides of a triangle? Answer 12,24,34 14,25,40 11,14,24 4,11,13

To determine which set of numbers could not represent the sides of a triangle, we need to apply the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.<br /><br />Let's check each set of numbers:<br /><br />1. $\{ 12,24,34\} $<br /> - $12 + 24 = 36 > 34$<br /> - $12 + 34 = 46 > 24$<br /> - $24 + 34 = 58 > 12$<br /> - All conditions satisfy the triangle inequality theorem.<br /><br />2. $\{ 14,25,40\} $<br /> - $14 + 25 = 39 < 40$<br /> - One condition does not satisfy the triangle inequality theorem.<br /><br />3. $\{ 11,14,24\} $<br /> - $11 + 14 = 25 > 24$<br /> - $11 + 24 = 35 > 14$<br /> - $14 + 24 = 38 > 11$<br /> - All conditions satisfy the triangle inequality theorem.<br /><br />4. $\{ 4,11,13\} $<br /> - $4 + 11 = 15 > 13$<br /> - $4 + 13 = 17 > 11$<br /> - $11 + 13 = 24 > 4$<br /> - All conditions satisfy the triangle inequality theorem.<br /><br />Therefore, the set of numbers $\{ 14,25,40\} $ could not represent the three sides of a triangle