If the unit of length is x meter then an area of `1m^(2)` will become

Options

A. x
B. 1/x
C. `x^(2)`
D. `1//x^(2)`

Answer

To solve the problem, we need to convert the area of 1 square meter into the new unit of area when the unit of length is defined as x meters. Here’s how we can do it step by step:

### Step-by-Step Solution:

1. **Understand the Units**:
- The standard unit of length in the SI system is 1 meter.
- According to the question, the new unit of length is defined as x meters.

2. **Convert 1 Meter to the New Unit**:
- Since 1 meter is equivalent to x meters in the new unit, we can express 1 meter as:
\[ 1 \text{ meter} = \frac{1}{x} \text{ new units} \]

3. **Calculate the Area in New Units**:
- The area in the SI system is given as 1 square meter (1 m²).
- To convert this area into the new unit, we need to square the conversion factor from meters to the new unit:
\[ \text{Area} = 1 \text{ m}^2 = 1 \left(\frac{1}{x} \text{ new units}\right)^2 \]

4. **Perform the Squaring**:
- Squaring the conversion factor gives:
\[ \text{Area} = 1 \cdot \left(\frac{1}{x}\right)^2 = \frac{1}{x^2} \text{ new units}^2 \]

5. **Final Result**:
- Therefore, the area of 1 m² in the new unit of area is:
\[ \frac{1}{x^2} \text{ new units}^2 \]

### Conclusion:
The area of 1 m² will become \(\frac{1}{x^2}\) in the new unit of area.