Which of the following sets of numbers could not represent the three sides of a right triangle? Answer 42,56,70 40,42,58 32,61,68 33,56,65

To determine which set of numbers could not represent the sides of a right triangle, we need to check if the Pythagorean theorem holds true for each set. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.<br /><br />Let's check each set of numbers:<br /><br />1. $\{ 42,56,70\} $<br /> - $42^2 + 56^2 = 1764 + 3136 = 4900$<br /> - $70^2 = 4900$<br /> - Since $42^2 + 56^2 = 70^2$, this set of numbers can represent the sides of a right triangle.<br /><br />2. $\{ 40,42,58\} $<br /> - $40^2 + 42^2 = 1600 + 1764 = 3364$<br /> - $58^2 = 3364$<br /> - Since $40^2 + 42^2 = 58^2$, this set of numbers can represent the sides of a right triangle.<br /><br />3. $\{ 32,61,68\} $<br /> - $32^2 + 61^2 = 1024 + 3721 = 4745$<br /> - $68^2 = 4624$<br /> - Since $32^2 + 61^2 \neq 68^2$, this set of numbers cannot represent the sides of a right triangle.<br /><br />4. $\{ 33,56,65\} $<br /> - $33^2 + 56^2 = 1089 + 3136 = 4225$<br /> - $65^2 = 4225$<br /> - Since $33^2 + 56^2 = 65^2$, this set of numbers can represent the sides of a right triangle.<br /><br />Therefore, the set of numbers that could not represent the sides of a right triangle is $\{ 32,61,68\} $.