If the length of the sides which make the right angle of a right angled triangle are 6 cm and 8 cm, what is the length of hypotenuse?

Options

A. 12 cm
B. 10cm
C. 14cm
D. 20cm

Answer

To find the length of the hypotenuse of a right-angled triangle where the lengths of the two sides that form the right angle are given as 6 cm and 8 cm, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

### Step-by-Step Solution:

1. **Identify the lengths of the sides**:
- Let side a = 6 cm (one side forming the right angle)
- Let side b = 8 cm (the other side forming the right angle)

2. **Apply the Pythagorean theorem**:
- According to the theorem, the relationship is given by:
\[ c^2 = a^2 + b^2 \]
- Here, c is the length of the hypotenuse.

3. **Substitute the values into the equation**:
- Substitute a = 6 cm and b = 8 cm into the equation:
\[ c^2 = 6^2 + 8^2 \]

4. **Calculate the squares of the sides**:
- Calculate \(6^2\):
\[ 6^2 = 36 \]
- Calculate \(8^2\):
\[ 8^2 = 64 \]

5. **Add the squares**:
- Now add the results:
\[ c^2 = 36 + 64 = 100 \]

6. **Find the length of the hypotenuse**:
- To find c, take the square root of both sides:
\[ c = \sqrt{100} = 10 \text{ cm} \]

### Final Answer:
The length of the hypotenuse is **10 cm**.

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