The area of a triangle is 615 `m^(2)`. If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.

Options

A. 15 metres
B. 12 metres
C. 10 metres
D. None of these

Answer

To find the length of the perpendicular dropped on the given side of the triangle, we can use the formula for the area of a triangle. The area of a triangle is given by the formula:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

Where:
- The base is one side of the triangle.
- The height (or altitude) is the perpendicular distance from the opposite vertex to the base.

### Step-by-step Solution:

1. **Identify the given values**:
- Area of the triangle (A) = 615 m²
- Length of the base (b) = 123 m

2. **Use the area formula**:
\[ A = \frac{1}{2} \times b \times h \]
Where \( h \) is the height (or perpendicular) we need to find.

3. **Substitute the known values into the formula**:
\[ 615 = \frac{1}{2} \times 123 \times h \]

4. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \times 615 = 123 \times h \]
\[ 1230 = 123 \times h \]

5. **Solve for \( h \)**:
\[ h = \frac{1230}{123} \]
\[ h = 10 \text{ m} \]

6. **Conclusion**:
The length of the perpendicular dropped on the side of 123 m from the opposite vertex is **10 m**.