Find the length and cost of canvas of width 90 cm required to cover a board 3.2m long and 1.35 m wide at the rate of ₹ 24 per metre?

Answer

To solve the problem of finding the length and cost of canvas required to cover a board, we will follow these steps:

### Step 1: Calculate the Area of the Board
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Given:
- Length of the board = 3.2 m
- Width of the board = 1.35 m

Calculating the area:
\[ \text{Area} = 3.2 \, \text{m} \times 1.35 \, \text{m} = 4.32 \, \text{m}^2 \]

### Step 2: Convert the Width of the Canvas to Meters
The width of the canvas is given in centimeters. We need to convert it to meters:
\[ \text{Width of canvas} = 90 \, \text{cm} = \frac{90}{100} \, \text{m} = 0.9 \, \text{m} \]

### Step 3: Calculate the Length of the Canvas Required
Since the area of the canvas must equal the area of the board, we can set up the equation:
\[ \text{Area of canvas} = \text{Length of canvas} \times \text{Width of canvas} \]
Let \( L \) be the length of the canvas. Then:
\[ 4.32 \, \text{m}^2 = L \times 0.9 \, \text{m} \]
To find \( L \):
\[ L = \frac{4.32 \, \text{m}^2}{0.9 \, \text{m}} = 4.8 \, \text{m} \]

### Step 4: Calculate the Cost of the Canvas
The cost is calculated using the formula:
\[ \text{Cost} = \text{Rate} \times \text{Length} \]
Given:
- Rate = ₹ 24 per meter
- Length of canvas = 4.8 m

Calculating the cost:
\[ \text{Cost} = 24 \, \text{₹/m} \times 4.8 \, \text{m} = 115.2 \, \text{₹} \]

### Final Results
- Length of the canvas required: **4.8 m**
- Cost of the canvas: **₹ 115.2**

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