Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: A) 4, 7, 9 B) 5, 12, 13 C) 20, 22, 24

Answer 1

Using the Pythagorean theorem, we find that only option B) 5, 12, 13 can form a right triangle. Options A) 4, 7, 9 and C) 20, 22, 24 do not meet the criteria for a right triangle's side lengths.

Step-by-step explanation:

Identifying Right Triangles Using the Pythagorean Theorem

To determine which sets of side lengths form a right triangle, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². When these sides are labeled in a problem, the hypotenuse is always the longest side.

Let us evaluate the given options:

1. 4, 7, 9: This cannot be a right triangle because 4² + 7² does not equal 9². (16 + 49 ≠ 81).
2. 5, 12, 13: This can be a right triangle because 5² + 12² equals 13². (25 + 144 = 169).
3. 20, 22, 24: This cannot be a right triangle because 20² + 22² does not equal 24². (400 + 484 ≠ 576).

Therefore, the only set of side lengths that forms a right triangle is B) 5, 12, 13.