The sides of a triangular farm are 20 m, 21 m and 29 m respectively. How much will be total expenses for cutting the crop at the rate of ₹ 15 per square meter?

Options

A. ₹ 2,100
B. ₹ 1,890
C. ₹ 3,150
D. ₹ 2,500

Answer

To solve the problem, we need to calculate the area of the triangular farm and then determine the total expenses for cutting the crop based on that area.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
The sides of the triangular farm are given as:
- \( a = 20 \, m \)
- \( b = 21 \, m \)
- \( c = 29 \, m \)

2. **Calculate the semi-perimeter (s)**:
The semi-perimeter \( s \) is calculated using the formula:
\[ s = \frac{a + b + c}{2} \]
Substituting the values:
\[ s = \frac{20 + 21 + 29}{2} = \frac{70}{2} = 35 \, m \]

3. **Use Heron's formula to find the area (A)**:
Heron's formula states that the area \( A \) of a triangle can be calculated as:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substituting the values:
\[ A = \sqrt{35(35-20)(35-21)(35-29)} \]
Simplifying the terms:
\[ A = \sqrt{35(15)(14)(6)} \]

4. **Calculate the products inside the square root**:
First, calculate \( 15 \times 14 \times 6 \):
\[ 15 \times 14 = 210 \]
\[ 210 \times 6 = 1260 \]
Now, multiply by 35:
\[ A = \sqrt{35 \times 1260} \]

5. **Calculate \( 35 \times 1260 \)**:
\[ 35 \times 1260 = 44100 \]
Now, take the square root:
\[ A = \sqrt{44100} = 210 \, m^2 \]

6. **Calculate the total expenses for cutting the crop**:
The cost of cutting the crop is given as ₹ 15 per square meter. Thus, the total expenses can be calculated as:
\[ \text{Total Expenses} = \text{Area} \times \text{Rate} \]
Substituting the values:
\[ \text{Total Expenses} = 210 \, m^2 \times 15 \, \text{₹/m}^2 = 3150 \, ₹ \]

### Final Answer:
The total expenses for cutting the crop will be **₹ 3150**.