The sides of a triangular field are 56 m, 90 m and 106 m. The cost of levelling the field at Rs 6.80 per `m^(2)` is :

Options

A. Rs 17,136
B. Rs 14, 616
C. Rs 20, 182
D. Rs 15, 112

Answer

To find the cost of leveling the triangular field with sides 56 m, 90 m, and 106 m, we first need to calculate the area of the triangle. Since it is a right triangle, we can use the formula for the area of a right triangle.

### Step-by-Step Solution:

**Step 1: Identify the sides of the triangle.**
- The sides of the triangle are given as 56 m, 90 m, and 106 m.
- Here, 106 m is the hypotenuse, and 56 m and 90 m are the other two sides.

**Step 2: Calculate the area of the triangle.**
- The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
- In this case, we can take the base as 56 m and the height as 90 m.
- Plugging in the values:
\[ A = \frac{1}{2} \times 56 \times 90 \]
- Calculate \( 56 \times 90 \):
\[ 56 \times 90 = 5040 \]
- Now, divide by 2:
\[ A = \frac{5040}{2} = 2520 \, m^2 \]

**Step 3: Calculate the cost of leveling the field.**
- The cost of leveling is given as Rs 6.80 per \( m^2 \).
- To find the total cost, multiply the area by the cost per square meter:
\[ \text{Total Cost} = \text{Area} \times \text{Cost per } m^2 \]
- Substituting the values:
\[ \text{Total Cost} = 2520 \times 6.80 \]
- Now, calculate \( 2520 \times 6.80 \):
\[ 2520 \times 6.80 = 17136 \]

**Final Answer:**
- The cost of leveling the field is Rs 17,136.