The problem involves finding the length of the hypotenuse of a right triangle where the two legs are given as $6 \, \text{cm}$ and $8 \, \text{cm}$. Let's solve it step by step using the Pythagorean Theorem:

Step 1: Write the Pythagorean Theorem

$c^2 = a^2 + b^2$ Here:

• $a = 6 \, \text{cm}$,
• $b = 8 \, \text{cm}$,
• $c$ is the hypotenuse.

Step 2: Substitute the values of $a$ and $b$

$c^2 = 6^2 + 8^2$ $c^2 = 36 + 64$ $c^2 = 100$

Step 3: Solve for $c$ by taking the square root

$c = \sqrt{100} = 10 \, \text{cm}.$

Final Answer:

The length of the hypotenuse is: $\boxed{10 \, \text{cm}}$

Would you like a breakdown of any specific step or additional related examples?

Related Questions:

1. How do you calculate the area of this triangle?
2. Can the triangle with sides $6 \, \text{cm}$, $8 \, \text{cm}$, and $10 \, \text{cm}$ be classified as a special triangle?
3. What is the perimeter of the triangle?
4. How does the Pythagorean Theorem work for non-right triangles?
5. Can the theorem be extended to find one of the legs if the hypotenuse and the other leg are given?

Tip:

For right triangles with integer side lengths, remember that they may form Pythagorean triples like $(3, 4, 5)$ or $(6, 8, 10)$. These help in quick verification.