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To determine which set of numbers could represent the sides of a right triangle, we will apply the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse (the longest side).

Let's evaluate each option:

1. **{32, 56, 65}**:
   \[
   32^2 + 56^2 = 1024 + 3136 = 4160
   \]
   \[
   65^2 = 4225
   \]
   \( 4160 \neq 4225 \), so this set does not satisfy the Pythagorean theorem.

2. **{42, 56, 70}**:
   \[
   42^2 + 56^2 = 1764 + 3136 = 4900
   \]
   \[
   70^2 = 4900
   \]
   \( 4900 = 4900 \), so this set satisfies the Pythagorean theorem.

3. **{44, 60, 75}**:
   \[
   44^2 + 60^2 = 1936 + 3600 = 5536
   \]
   \[
   75^2 = 5625
   \]
   \( 5536 \neq 5625 \), so this set does not satisfy the Pythagorean theorem.

4. **{10, 40, 41}**:
   \[
   10^2 + 40^2 = 100 + 1600 = 1700
   \]
   \[
   41^2 = 1681
   \]
   \( 1700 \neq 1681 \), so this set does not satisfy the Pythagorean theorem.

The correct answer is **{42, 56, 70}**.

Would you like further details, or have any other questions?

### Follow-up Questions:
1. What is the Pythagorean theorem, and why is it important?
2. How can you determine if a set of numbers represents a right triangle?
3. Can the Pythagorean theorem be used for non-right triangles?
4. What are some real-life applications of the Pythagorean theorem?
5. How do you calculate the length of a missing side of a right triangle using the Pythagorean theorem?

### Tip:
Always remember that the hypotenuse is the longest side of a right triangle and opposite the right angle.

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

Learn how to determine which set of numbers can represent the sides of a right triangle by applying the Pythagorean theorem. Evaluate options such as {32, 56, 65}, {42, 56, 70}, and others. Suitable for students in Grades 8-10.

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