If the angles of a triangle are in the ratio 3:4:5, then the triangle formed will be

Options

A. Right angled triangle
B. Isosceles triangle
C. Scalene triangle
D. Obtuse angled triangle

Answer

To determine the type of triangle formed by the angles in the ratio 3:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio of Angles**:
The angles of the triangle are given in the ratio of 3:4:5. This means we can express the angles as:
- Angle A = 3x
- Angle B = 4x
- Angle C = 5x

2. **Use the Triangle Angle Sum Property**:
The sum of the angles in any triangle is always 180 degrees. Therefore, we can set up the equation:
\[ 3x + 4x + 5x = 180 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 12x = 180 \]

4. **Solve for x**:
To find the value of x, divide both sides of the equation by 12:
\[ x = \frac{180}{12} = 15 \]

5. **Calculate Each Angle**:
Now that we have the value of x, we can find each angle:
- Angle A = 3x = 3(15) = 45 degrees
- Angle B = 4x = 4(15) = 60 degrees
- Angle C = 5x = 5(15) = 75 degrees

6. **Identify the Type of Triangle**:
Now we have the angles: 45 degrees, 60 degrees, and 75 degrees.
- Since all angles are less than 90 degrees, this triangle is not a right triangle.
- Since all angles are different, it is not an isosceles triangle.
- Since all angles are less than 90 degrees, it is not an obtuse triangle.
- Therefore, the triangle is classified as an **acute triangle**.

### Conclusion:
The triangle formed by the angles in the ratio 3:4:5 is an **acute triangle**.