A design on a floor is made up of triangular tiles. The sides of each triangle being 24 cm, 32 cm and 40 cm. Find the cost of polishing all 170 tiles on the floor at the rate of Rs.1.50 per `cm^(2)`.

Options

A. Rs.97920
B. Rs.65280
C. Rs. 99480
D. Rs.89460

Answer

To solve the problem, we need to find the area of one triangular tile and then calculate the cost of polishing all 170 tiles based on the area. Here’s the step-by-step solution:

### Step 1: Identify the sides of the triangle
The sides of the triangle are given as:
- a = 24 cm
- b = 32 cm
- c = 40 cm

### Step 2: Check if the triangle is a right triangle
To check if the triangle is a right triangle, we can use the Pythagorean theorem:
- \( a^2 + b^2 = c^2 \)
- \( 24^2 + 32^2 = 40^2 \)
- \( 576 + 1024 = 1600 \)
- \( 1600 = 1600 \) (True)

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

### Step 3: Calculate the area of the triangle
The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take 24 cm as the base and 32 cm as the height.
\[ A = \frac{1}{2} \times 24 \times 32 \]
\[ A = \frac{1}{2} \times 768 \]
\[ A = 384 \, \text{cm}^2 \]

### Step 4: Calculate the total area for 170 tiles
To find the total area for 170 tiles, we multiply the area of one tile by the number of tiles:
\[ \text{Total Area} = 384 \, \text{cm}^2 \times 170 \]
\[ \text{Total Area} = 65280 \, \text{cm}^2 \]

### Step 5: Calculate the cost of polishing
The cost of polishing is given as Rs. 1.50 per cm². Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Total Area} \times \text{Cost per cm}^2 \]
\[ \text{Total Cost} = 65280 \, \text{cm}^2 \times 1.50 \]
\[ \text{Total Cost} = 97920 \, \text{Rs} \]

### Final Answer
The total cost of polishing all 170 tiles is **Rs. 97920**.

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