In measuring the sides of a recangle, there is an excess of 5% on one side and 2% deficit on the other. Then the error percent in the area is

Options

A. `3.3%`
B. `3.0%`
C. `2.9%`
D. `2.7%`

Answer

To solve the problem of finding the error percentage in the area of a rectangle with given measurement errors, we can follow these steps:

### Step 1: Understand the Problem
We have a rectangle where one side has a 5% excess and the other side has a 2% deficit. We need to find the error percentage in the area of the rectangle.

### Step 2: Define the Original Dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

### Step 3: Calculate the New Dimensions
- The length with a 5% excess can be calculated as:
\[ L' = L + 0.05L = 1.05L \]
- The breadth with a 2% deficit can be calculated as:
\[ B' = B - 0.02B = 0.98B \]

### Step 4: Calculate the Original Area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 5: Calculate the New Area
The new area \( A' \) with the adjusted dimensions is:
\[ A' = L' \times B' = (1.05L) \times (0.98B) = 1.05 \times 0.98 \times L \times B \]
Calculating \( 1.05 \times 0.98 \):
\[ 1.05 \times 0.98 = 1.029 \]
Thus,
\[ A' = 1.029 \times A \]

### Step 6: Calculate the Error in Area
The error in area can be calculated as:
\[ \text{Error} = A' - A = (1.029A - A) = 0.029A \]

### Step 7: Calculate the Error Percentage
The error percentage in the area is given by:
\[ \text{Error Percentage} = \left( \frac{\text{Error}}{A} \right) \times 100 = \left( \frac{0.029A}{A} \right) \times 100 = 2.9\% \]

### Final Answer
The error percentage in the area of the rectangle is **2.9%**.

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