Sharel wants to build a right triangle. Which of these sets of sides would NOT work? 56,33,65 63,16,65 85,40,75 39,40,9

To determine which set of sides would not work for building 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 sides:<br /><br />1. $\{ 56,33,65\} $<br /> - Hypotenuse: 65<br /> - Check: $56^2 + 33^2 = 65^2$<br /> - Calculation: $3136 + 1089 = 4225$<br /> - Result: $4225 = 4225$ (True)<br /><br />2. $\{ 63,16,65\} $<br /> - Hypotenuse: 65<br /> - Check: $63^2 + 16^2 = 65^2$<br /> - Calculation: $3969 + 256 = 4225$<br /> - Result: $4225 = 4225$ (True)<br /><br />3. $\{ 85,40,75\} $<br /> - Hypotenuse: 85<br /> - Check: $40^2 + 75^2 = 85^2$<br /> - Calculation: $1600 + 5625 = 7225$<br /> - Result: $7225 = 7225$ (True)<br /><br />4. $\{ 39,40,9\} $<br /> - Hypotenuse: 40<br /> - Check: $39^2 + 9^2 = 40^2$<br /> - Calculation: $1521 + 81 = 1602$<br /> - Result: $1602 \neq 1600$ (False)<br /><br />Therefore, the set of sides $\{ 39,40,9\} $ would not work for building a right triangle.