Three sides of a triangular field are of length 15 m, 20 m and 25 m long respectively. Find the cost of sowing seeds in the field at the rate of 5 rupees per sq.m.

Options

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

Answer

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

### Step 1: Identify the sides of the triangle
The sides of the triangular field are given as:
- Side 1 (a) = 15 m
- Side 2 (b) = 20 m
- Side 3 (c) = 25 m

### Step 2: Check if the triangle is a right triangle
To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Here, we check:
- \( a^2 + b^2 = c^2 \)
- \( 15^2 + 20^2 = 25^2 \)
- \( 225 + 400 = 625 \)
- \( 625 = 625 \)

Since the equation holds true, the triangle is indeed a right triangle.

### Step 3: Calculate the area of the triangle
For a right triangle, the area can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, we can take:
- Base = 15 m
- Height = 20 m

Now, substituting the values:
\[ \text{Area} = \frac{1}{2} \times 15 \times 20 = \frac{1}{2} \times 300 = 150 \text{ m}^2 \]

### Step 4: Calculate the cost of sowing seeds
The cost of sowing seeds is given at the rate of 5 rupees per square meter. Therefore, we can calculate the total cost as follows:
\[ \text{Cost} = \text{Area} \times \text{Rate} \]
Substituting the values:
\[ \text{Cost} = 150 \text{ m}^2 \times 5 \text{ rupees/m}^2 = 750 \text{ rupees} \]

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

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