Step-by-step The side lengths of a right triangle must satisfy the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Therefore, any measurement that does not satisfy this equation cannot represent the side lengths of a right triangle. For example, let's consider the measurements 3, 4, and 7. If we apply the Pythagorean theorem, we have: 3^2 + 4^2 = 9 + 16 = 25 7^2 = 49 Since 25 is not equal to 49, these measurements do not satisfy the Pythagorean theorem and therefore cannot represent the side lengths of a right triangle. In general, any set of measurements that do not satisfy the Pythagorean theorem, such as 2, 2, and 5 or 6, 8, and 10, would not represent the side lengths of a right triangle. It's important to note that the Pythagorean theorem is a fundamental concept in geometry and is used to determine if a triangle is a right triangle or not. By applying this theorem, you can identify whether a set of measurements can form a right triangle or not.