The cost of leveling a triangular piece of land whoses sides are 72 m , 30 m and 78 m respectively at the rate of 20 paisa per square metre is :

Options

A. Rs. 220
B. Rs. 200
C. Rs. 216
D. Rs. 210

Answer

To solve the problem step by step, we will first find the area of the triangular piece of land using the given sides, and then calculate the cost of leveling based on that area.

### Step 1: Identify the sides of the triangle
The sides of the triangle are given as:
- Side A = 72 m
- Side B = 30 m
- Side C = 78 m

### Step 2: Check if the triangle is a right triangle
We can check if the triangle is a right triangle using the Pythagorean theorem:
\[ A^2 + B^2 = C^2 \]
Calculating:
- \( 72^2 = 5184 \)
- \( 30^2 = 900 \)
- \( 78^2 = 6084 \)

Now, check:
\[ 72^2 + 30^2 = 5184 + 900 = 6084 \]
Since \( 6084 = 78^2 \), 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:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take 72 m as the base and 30 m as the height.
\[ \text{Area} = \frac{1}{2} \times 72 \times 30 \]
Calculating:
\[ \text{Area} = \frac{1}{2} \times 2160 = 1080 \, \text{m}^2 \]

### Step 4: Calculate the cost of leveling
The cost of leveling is given at the rate of 20 paisa per square meter. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Area} \times \text{Rate} \]
Substituting the values:
\[ \text{Cost} = 1080 \times 20 \]
Calculating:
\[ \text{Cost} = 21600 \, \text{paisa} \]

### Step 5: Convert paisa to rupees
Since 1 rupee = 100 paisa:
\[ \text{Cost in rupees} = \frac{21600}{100} = 216 \, \text{rupees} \]

### Final Answer
The cost of leveling the triangular piece of land is **216 rupees**.

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