# If the length and breadth of a plane are (40 + 0.2) and (30 ± 0.1) cm, the absolute error in the measurement of area is: A. 10 cm^2 B. 8 cm^2 C. 9 cm^2 D. 7 cm^2

## Question

If the length and breadth of a plane are $(40 + 0.2)$ and $(30 \pm 0.1)$ cm, the absolute error in the measurement of area is:

A. $10 ~\text{cm}^2$

B. $8 ~\text{cm}^2$

C. $9 ~\text{cm}^2$

D. $7 ~\text{cm}^2$

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## Answer

To solve for the absolute error in the area given the length and breadth with their respective errors, we can follow the steps below:

### Given:

**Length**($L \pm \Delta L$) = $40 \pm 0.2$ cm**Breadth**($B \pm \Delta B$) = $30 \pm 0.1$ cm

### Steps to :

**Calculate the area without errors**: The nominal area ($A$) is calculated by: $$ A = L \times B = 40 \times 30 = 1200 \ \text{cm}^2 $$**Understand the error in areas**: The absolute error in area ($\Delta A$) can be determined using the formula: $$ \frac{\Delta A}{A} = \frac{\Delta L}{L} + \frac{\Delta B}{B} $$**Substitute the given values**:$\Delta L = 0.2$ cm

$L = 40$ cm

$\Delta B = 0.1$ cm

$B = 30$ cm

Using formula: $$ \frac{\Delta A}{1200} = \frac{0.2}{40} + \frac{0.1}{30} $$

**Calculate the terms on the right-hand side**:$\frac{0.2}{40} = 0.005$

$\frac{0.1}{30} \approx 0.00333$

Adding these: $$ \frac{\Delta A}{1200} = 0.005 + 0.00333 = 0.00833 $$

**Calculate the absolute error**: $$ \Delta A = 1200 \times 0.00833 \approx 10 \ \text{cm}^2 $$

### Final Answer

The absolute error in the measurement of the area is **10 cm²**.

So, the correct option is **Option A**.

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