The length and breadth of a table are `(125+-0.4)cm` and `(75+-0.5)cm` respectively. What is the area of the table?

Explanation

To find the area of the table given its length and breadth with uncertainties, we will follow these steps:

### Step 1: Identify the given values
- Length (L) = \( 125 \pm 0.4 \) cm
- Breadth (B) = \( 75 \pm 0.5 \) cm

### Step 2: Calculate the area
The area (A) of the table can be calculated using the formula:
\[ A = L \times B \]
Substituting the values:
\[ A = 125 \, \text{cm} \times 75 \, \text{cm} = 9375 \, \text{cm}^2 \]

### Step 3: Determine the uncertainties in the area
To find the uncertainty in the area (\( \Delta A \)), we can use the formula for the propagation of uncertainties for multiplication:
\[ \frac{\Delta A}{A} = \frac{\Delta L}{L} + \frac{\Delta B}{B} \]
Where:
- \( \Delta L = 0.4 \) cm (uncertainty in length)
- \( \Delta B = 0.5 \) cm (uncertainty in breadth)

### Step 4: Substitute the values into the uncertainty formula
Substituting the values we have:
\[ \frac{\Delta A}{9375} = \frac{0.4}{125} + \frac{0.5}{75} \]

Calculating each term:
\[ \frac{0.4}{125} = 0.0032 \quad \text{and} \quad \frac{0.5}{75} = 0.00667 \]

Adding these together:
\[ \frac{\Delta A}{9375} = 0.0032 + 0.00667 = 0.00987 \]

### Step 5: Calculate \( \Delta A \)
Now, we can find \( \Delta A \):
\[ \Delta A = 9375 \times 0.00987 \approx 92.5 \, \text{cm}^2 \]

### Step 6: Write the final result
Thus, the area of the table with its uncertainty is:
\[ A = 9375 \pm 92.5 \, \text{cm}^2 \]

### Summary
The area of the table is \( 9375 \pm 92.5 \, \text{cm}^2 \).

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