ABC is a triangle in which BC = 10 cm, CA = 6 cm and AB = 8 cm, Which one of the following is a correct?

Options

A. ABC is an acute angled triangle
B. ABC is an obtuse angled triangle
C. ABC is an right angled triangle
D. None of the above

Answer

To determine the type of triangle ABC, we will use the given side lengths and apply the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- BC = 10 cm (let's denote this as side c)
- CA = 6 cm (let's denote this as side a)
- AB = 8 cm (let's denote this as side b)

2. **Calculate the squares of the sides**:
- Calculate \( BC^2 \):
\[ BC^2 = 10^2 = 100 \, \text{cm}^2 \]
- Calculate \( CA^2 \):
\[ CA^2 = 6^2 = 36 \, \text{cm}^2 \]
- Calculate \( AB^2 \):
\[ AB^2 = 8^2 = 64 \, \text{cm}^2 \]

3. **Apply the Pythagorean theorem**:
- According to the Pythagorean theorem, for a triangle to be a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side:
\[ a^2 + b^2 = c^2 \]
- Substitute the values:
\[ CA^2 + AB^2 = BC^2 \]
\[ 36 + 64 = 100 \]

4. **Check the equality**:
- Calculate \( 36 + 64 \):
\[ 36 + 64 = 100 \]
- Since \( 100 = 100 \), this confirms that:
\[ CA^2 + AB^2 = BC^2 \]

5. **Conclusion**:
- Since the sum of the squares of the two shorter sides equals the square of the longest side, triangle ABC is a right-angled triangle.

### Final Answer:
Triangle ABC is a right-angled triangle.