If the area of the rectangle is `16 m^(2)`, then which of the following may not be the possible dimensions for rectangle ?

Options

A. Length = 8 m, breadth = 2 m
B. Length = 16 m, breadth = 1 m
C. Length = 32 m, breadth = `(1)/(2)m`
D. Length = 8.5 m, breadth = 2 m

Answer

To determine which of the given dimensions may not be possible for a rectangle with an area of 16 m², we will analyze each option by using the formula for the area of a rectangle:

**Area of a rectangle = Length × Breadth**

Given that the area is 16 m², we can set up the equation:

\[ L \times B = 16 \]

Now, let's evaluate each option:

1. **Option 1: Length = 8 m, Breadth = 2 m**
\[ 8 \times 2 = 16 \, \text{m}^2 \]
This is a valid dimension.

2. **Option 2: Length = 16 m, Breadth = 1 m**
\[ 16 \times 1 = 16 \, \text{m}^2 \]
This is also a valid dimension.

3. **Option 3: Length = 32 m, Breadth = 0.5 m (1/2 m)**
\[ 32 \times 0.5 = 16 \, \text{m}^2 \]
This is a valid dimension as well.

4. **Option 4: Length = 8.5 m, Breadth = 2 m**
\[ 8.5 \times 2 = 17 \, \text{m}^2 \]
This does not equal 16 m², hence it is not a valid dimension.

Thus, the option that may not be a possible dimension for the rectangle is:

**Answer: Option 4 (Length = 8.5 m, Breadth = 2 m)**

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