The problem asks which of the given sets of numbers could represent the three sides of a right triangle. We need to check if the Pythagorean theorem holds for each set of numbers, where the largest number is the hypotenuse.

1. Problem Description

The problem asks which of the given sets of numbers could represent the three sides of a right triangle. We need to check if the Pythagorean theorem holds for each set of numbers, where the largest number is the hypotenuse.

2. Solution Steps

We will use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $c$ is the largest side.

A. {13, 48, 50}

$13^2 + 48^2 = 169 + 2304 = 2473$

$50^2 = 2500$

Since $2473 \neq 2500$, this set does not represent a right triangle.

B. {49, 55, 73}

$49^2 + 55^2 = 2401 + 3025 = 5426$

$73^2 = 5329$

Since $5426 \neq 5329$, this set does not represent a right triangle.

C. {16, 63, 65}

$16^2 + 63^2 = 256 + 3969 = 4225$

$65^2 = 4225$

Since $4225 = 4225$, this set represents a right triangle.

D. {20, 72, 75}

$20^2 + 72^2 = 400 + 5184 = 5584$

$75^2 = 5625$

Since $5584 \neq 5625$, this set does not represent a right triangle.

3. Final Answer

C. {16, 63, 65}