Answer:
{39, 52, 64}
Step-by-step explanation:
The set of numbers that could not represent the three sides of a right triangle is {39, 52, 64}. To determine if a set of numbers can represent the sides of a right triangle, we can use the Pythagorean Theorem. According to the theorem, for a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
For each set:
1. {42, 56, 70}: \(42^2 + 56^2 = 1764 + 3136 = 4900\), \(70^2 = 4900\) (Pythagorean Theorem holds).
2. {36, 77, 85}: \(36^2 + 77^2 = 1296 + 5929 = 7225\), \(85^2 = 7225\) (Pythagorean Theorem holds).
3. {3, 4, 5}: \(3^2 + 4^2 = 9 + 16 = 25\), \(5^2 = 25\) (Pythagorean Theorem holds).
4. {39, 52, 64}: \(39^2 + 52^2 = 1521 + 2704 = 4225\), \(64^2 = 4096\) (Pythagorean Theorem does not hold).
Therefore, the set {39, 52, 64} could not represent the three sides of a right triangle.
