To determine which sets of side lengths can form a right triangle, we need to apply the Pythagorean Theorem, which states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides:

$a^2 + b^2 = c^2$ where $c$ is the hypotenuse (the longest side) and $a$ and $b$ are the other two sides.

Let’s check each set of side lengths:

1. 6 cm, 8 cm, 10 cm: $6^2 + 8^2 = 36 + 64 = 100$ $10^2 = 100$ Since $36 + 64 = 100$, this is a right triangle.

2. 14 cm, 18 cm, 20 cm: $14^2 + 18^2 = 196 + 324 = 520$ $20^2 = 400$ Since $520 \neq 400$, this is not a right triangle.

3. 20 cm, 21 cm, 29 cm: $20^2 + 21^2 = 400 + 441 = 841$ $29^2 = 841$ Since $400 + 441 = 841$, this is a right triangle.

4. 6 cm, 6 cm, 6 cm: This is an equilateral triangle, and none of the sides would satisfy the Pythagorean theorem, because all sides are equal. Thus, this cannot be a right triangle.

5. 10 cm, 24 cm, 26 cm: $10^2 + 24^2 = 100 + 576 = 676$ $26^2 = 676$ Since $100 + 576 = 676$, this is a right triangle.

Summary of correct answers:

• 6 cm, 8 cm, 10 cm
• 20 cm, 21 cm, 29 cm
• 10 cm, 24 cm, 26 cm

Would you like more details or have any questions?

Related questions:

1. What is the Pythagorean theorem, and how is it applied?
2. How do we calculate the hypotenuse of a right triangle?
3. What is an equilateral triangle, and how does it differ from a right triangle?
4. How can we identify the hypotenuse in a set of triangle side lengths?
5. Can a triangle have more than one right angle? Why or why not?

Tip: Always identify the longest side first when applying the Pythagorean theorem, as it is the hypotenuse.