Three sides of a triangular field are of length 15m, 20m and 25m long, respectively. Find the cost of sowing seeds in the field at the rate of `X5` per sqm.

Options

A. 750
B. 150
C. 300
D. 600

Answer

To solve the problem, we need to find the area of the triangular field first and then calculate the cost of sowing seeds based on that area. Here’s the step-by-step solution:

### Step 1: Identify the sides of the triangle
The lengths of the sides of the triangular field are given as:
- Side a = 15 m
- Side b = 20 m
- Side c = 25 m

### Step 2: Calculate the semi-perimeter (s)
The semi-perimeter (s) of the triangle can be calculated using the formula:
\[ s = \frac{a + b + c}{2} \]
Substituting the values:
\[ s = \frac{15 + 20 + 25}{2} = \frac{60}{2} = 30 \, \text{m} \]

### Step 3: Use Heron's formula to find the area (A)
Heron's formula for the area of a triangle is given by:
\[ A = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} \]
Substituting the values we have:
\[ A = \sqrt{30 \cdot (30 - 15) \cdot (30 - 20) \cdot (30 - 25)} \]
\[ A = \sqrt{30 \cdot 15 \cdot 10 \cdot 5} \]

### Step 4: Simplify the expression under the square root
Calculating the values:
\[ A = \sqrt{30 \cdot 15 \cdot 10 \cdot 5} \]
First, calculate \( 30 \cdot 15 = 450 \)
Then, calculate \( 10 \cdot 5 = 50 \)
Now, multiply these results:
\[ 450 \cdot 50 = 22500 \]
Now, take the square root:
\[ A = \sqrt{22500} = 150 \, \text{m}^2 \]

### Step 5: Calculate the cost of sowing seeds
The cost of sowing seeds is given at the rate of 5 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Area} \times \text{Cost per sqm} \]
\[ \text{Total Cost} = 150 \, \text{m}^2 \times 5 \, \text{per sqm} = 750 \]

### Final Answer
The cost of sowing seeds in the field is **750**.

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