#### The Pythagorean Theorem

Which set of numbers could represent the lengths of the sides of a right triangle?

O 16, 32, 36

O 8, 12, 16

5, 12, 13

6, 7, 8

**Answer:**

The set of numbers that could represent the lengths of the sides of a right triangle are 5, 12, 13.

**Explanation:**

The set of numbers that could represent the lengths of the sides of a right triangle are 5, 12, 13.

This is because these numbers satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, for a right triangle with sides a, b, and c (where c is the hypotenuse), the equation would be a^2 + b^2 = c^2.

Let’s check if the given options satisfy this condition:

16^2 + 32^2 = 256 + 1024 = 1280 ≠ 36^2

8^2 + 12^2 = 64 + 144 = 208 ≠ 16^2

5^2 + 12^2 = 25 + 144 = 169 = 13^2 ✔

6^2 + 7^2 = 36 + 49 = 85 ≠ 8^2

Therefore, the only set of numbers that satisfies the Pythagorean theorem and could represent the lengths of the sides of a right triangle is 5, 12, 13.

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