The SI unit of length is the meter. Suppose we adopt a new unit of length which equals to x meters. The area 1m2 expressed in terms of the new unit has a magnitude-

Options

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

Answer

To solve the problem, we need to express the area of 1 square meter in terms of a new unit of length that is defined as \( x \) meters. Here’s the step-by-step solution:

### Step 1: Understand the relationship between the old and new units
The SI unit of length is the meter (1 m). We are defining a new unit of length, which we will denote as \( U \), such that:
\[ U = x \, \text{meters} \]

### Step 2: Find the conversion factor for the new unit
To express the new unit in terms of meters, we can say:
\[ 1 \, U = x \, \text{meters} \]
Thus, to convert from the new unit back to meters, we have:
\[ 1 \, \text{meter} = \frac{1}{x} \, U \]

### Step 3: Calculate the area in the new unit
The area in the SI system is given as \( 1 \, \text{m}^2 \). To express this area in terms of the new unit \( U \), we need to convert meters to the new unit:
\[ 1 \, \text{m}^2 = (1 \, \text{m}) \times (1 \, \text{m}) \]

Substituting the conversion factor:
\[ 1 \, \text{m}^2 = \left(\frac{1}{x} \, U\right) \times \left(\frac{1}{x} \, U\right) \]
\[ 1 \, \text{m}^2 = \frac{1}{x^2} \, U^2 \]

### Step 4: Express the area in terms of the new unit
From the above calculation, we can conclude that:
\[ 1 \, \text{m}^2 = \frac{1}{x^2} \, U^2 \]

This means that the area of \( 1 \, \text{m}^2 \) expressed in terms of the new unit \( U \) has a magnitude of:
\[ \frac{1}{x^2} \]

### Final Answer
Thus, the area \( 1 \, \text{m}^2 \) expressed in terms of the new unit has a magnitude of:
\[ \frac{1}{x^2} \]