Question

Which of the following sets of numbers could not represent the three sides of a right triangle?

Option 1: {40, 75, 85}
Option 2: {40, 42, 59}
Option 3: {28, 45, 53}
Option 4: {9, 12, 15}

Answer 1

To identify which set of numbers cannot represent the sides of a right triangle, the Pythagorean theorem was applied to each set. It was found that Option 2 ({40, 42, 59}) does not satisfy the equation a² + b² = c², and therefore, cannot represent the sides of a right triangle.

Step-by-step explanation:

The question is asking which set of three numbers cannot represent the lengths of the sides of a right triangle. To determine if a set of numbers can represent a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with sides of lengths a, b, and c, where c is the hypotenuse, the following must be true: a² + b² = c².

Let's evaluate each option:

• Option 1: {40, 75, 85} - 40² + 75² = 1600 + 5625 = 7225, which is not equal to 85² (7225).
• Option 2: {40, 42, 59} - 40² + 42² = 1600 + 1764 = 3364, which is not equal to 59² (3481).
• Option 3: {28, 45, 53} - 28² + 45² = 784 + 2025 = 2809, which is equal to 53² (2809), so this set can represent a right triangle.
• Option 4: {9, 12, 15} - 9² + 12² = 81 + 144 = 225, which is equal to 15² (225), so this set can also represent a right triangle.

The set of numbers in Option 2 does not satisfy the conditions of the Pythagorean theorem for a right triangle, and thus cannot represent the sides of a right triangle.