Explanation:

To solve this, we first need to find the area of the triangular field using Heron's formula. Here's the breakdown:

- Heron's Formula:

Calculate the semi-perimeter (\(s\)) of the triangle:

$$

s = \frac{120 + 170 + 250}{2} = 270 \, \text{m}

$$

- Area Calculation:

$$

\text{Area} = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{270(270-120)(270-170)(270-250)} = \sqrt{270 \cdot 150 \cdot 100 \cdot 20}

$$

Simplify to find the area:

$$

\text{Area} \approx 9,000 \, \text{m}^2

$$

- Cost Calculation:

The cost to level the field is 7.40 Rs/m²:

$$

\text{Total Cost} = 9000 \times 7.40 = 66,600 \, \text{Rs}

$$

- Summary:

- Option 1: Rs65,120

- Option 2: Rs63,640

- Option 3: Rs59,200

- Option 4: Rs66,600 (Correct Answer)