Question

"Which of the following sets of numbers could represent the three sides of a right triangle?

{22,28,35}
\{5,12,13\}
\{25,70,74\}
\{48,56,73\}

Answer 1

The set {5,12,13} can represent the sides of a right triangle.

Step-by-step explanation:

A right triangle is a triangle that has one angle measuring 90 degrees. 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, if a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides (legs) of the triangle, and c is the length of the longest side (hypotenuse), then the set of numbers can represent the sides of a right triangle.

Let's examine the given sets of numbers:

1. {22,28,35}: 22^2 + 28^2 = 484 + 784 = 1268 ≠ 35^2 = 1225. This set of numbers does not satisfy the Pythagorean theorem and therefore, cannot represent the sides of a right triangle.
2. {5,12,13}: 5^2 + 12^2 = 25 + 144 = 169 = 13^2. This set of numbers satisfies the Pythagorean theorem and can represent the sides of a right triangle.
3. {25,70,74}: 25^2 + 70^2 = 625 + 4900 = 5525 ≠ 74^2 = 5476. This set of numbers does not satisfy the Pythagorean theorem and cannot represent the sides of a right triangle.
4. {48,56,73}: 48^2 + 56^2 = 2304 + 3136 = 5440 ≠ 73^2 = 5329. This set of numbers does not satisfy the Pythagorean theorem and cannot represent the sides of a right triangle.

Therefore, the set {5,12,13} can represent the sides of a right triangle.