The sides of a triangle are 12 cm, 8 cm and 6 cm respectively, the triangle is :

Options

A. acute
B. obtuse
C. right
D. can't be determined

Answer

To determine the type of triangle formed by the sides measuring 12 cm, 8 cm, and 6 cm, we can use the properties of triangles related to the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
Let the sides of the triangle be:
- \( a = 6 \) cm
- \( b = 8 \) cm
- \( c = 12 \) cm (the longest side)

2. **Check the Pythagorean theorem**:
According to the Pythagorean theorem, for a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the following conditions hold:
- If \( a^2 + b^2 = c^2 \), the triangle is a right triangle.
- If \( a^2 + b^2 > c^2 \), the triangle is acute.
- If \( a^2 + b^2 < c^2 \), the triangle is obtuse.

3. **Calculate \( a^2 + b^2 \)**:
\[ a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100 \]

4. **Calculate \( c^2 \)**:
\[ c^2 = 12^2 = 144 \]

5. **Compare \( a^2 + b^2 \) with \( c^2 \)**:
\[ 100 < 144 \]
Since \( a^2 + b^2 < c^2 \), we conclude that the triangle is obtuse.

### Conclusion:
The triangle with sides 12 cm, 8 cm, and 6 cm is an **obtuse triangle**.