Which of the following sets of numbers could not represent the three sides of a r triangle? Answer 24,32,40 12,16,20 30,40,51 20,21,29

To determine which set of numbers could not represent the sides of a triangle, we need to apply the Triangle Inequality Theorem. This 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. $\{ 24,32,40\} $<br /> - 24 + 32 > 40 (56 > 40, true)<br /> - 24 + 40 > 32 (64 > 32, true)<br /> - 32 + 40 > 24 (72 > 24, true)<br /> - This set satisfies the Triangle Inequality Theorem.<br /><br />2. $\{ 12,16,20\} $<br /> - 12 + 16 > 20 (28 > 20, true)<br /> - 12 + 20 > 16 (32 > 16, true)<br /> - 16 + 20 > 12 (36 > 12, true)<br /> - This set satisfies the Triangle Inequality Theorem.<br /><br />3. $\{ 30,40,51\} $<br /> - 30 + 40 > 51 (70 > 51, true)<br /> - 30 + 51 > 40 (81 > 40, true)<br /> - 40 + 51 > 30 (91 > 30, true)<br /> - This set satisfies the Triangle Inequality Theorem.<br /><br />4. $\{ 20,21,29\} $<br /> - 20 + 21 > 29 (41 > 29, true)<br /> - 20 + 29 > 21 (49 > 21, true)<br /> - 21 + 29 > 20 (50 > 20, true)<br /> - This set satisfies the Triangle Inequality Theorem.<br /><br />Therefore, all the given sets of numbers could represent the sides of a triangle.