A sheet in the form of a rhombus whose diagonals are 10 m and 8 m. The cost of painting both of its surfaces at the rate of Rs 70 per `m^(2)` is

Options

A. Rs 5600
B. Rs 4000
C. Rs 2800
D. Rs 2000

Answer

To solve the problem of finding the cost of painting a rhombus with given diagonals, we will follow these steps:

### Step 1: Identify the diagonals of the rhombus
The diagonals of the rhombus are given as:
- \( d_1 = 10 \, \text{m} \)
- \( d_2 = 8 \, \text{m} \)

### Step 2: Calculate the area of the rhombus
The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]
Substituting the values of the diagonals:
\[ A = \frac{1}{2} \times 10 \times 8 \]
\[ A = \frac{1}{2} \times 80 = 40 \, \text{m}^2 \]

### Step 3: Calculate the total area to be painted
Since both surfaces of the rhombus need to be painted, the total area \( A_{total} \) is:
\[ A_{total} = 2 \times A = 2 \times 40 = 80 \, \text{m}^2 \]

### Step 4: Calculate the cost of painting
The cost of painting is given at the rate of Rs. 70 per \( \text{m}^2 \). Therefore, the total cost \( C \) can be calculated as:
\[ C = A_{total} \times \text{cost per m}^2 \]
Substituting the values:
\[ C = 80 \times 70 \]
\[ C = 5600 \, \text{Rs} \]

### Final Answer
The cost of painting both surfaces of the rhombus is Rs. 5600.

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