To understand what the expression [tex]\((20 - w) w\)[/tex] represents, let's carefully analyze the given information and perform step-by-step calculations.
1. Start with the given perimeter:
- The perimeter [tex]\(P\)[/tex] of a rectangle is given as 40 meters.
- The formula for the perimeter of a rectangle is [tex]\(P = 2 \times (\text{length} + \text{width})\)[/tex].
2. Formulate the equation:
- According to the formula and given perimeter:
[tex]\[
40 = 2 \times (\text{length} + \text{width})
\][/tex]
3. Simplify the equation:
- Divide both sides by 2:
[tex]\[
20 = \text{length} + \text{width}
\][/tex]
- We are given [tex]\(w\)[/tex] as the width of the garden in meters, so:
[tex]\[
\text{length} = 20 - \text{width} = 20 - w
\][/tex]
4. Calculate the area of the garden:
- The area [tex]\(A\)[/tex] of a rectangle is given by the product of its length and width:
[tex]\[
A = \text{length} \times \text{width}
\][/tex]
- Substitute the values for length and width:
[tex]\[
A = (20 - w) \times w
\][/tex]
Therefore, the expression [tex]\((20 - w) w\)[/tex] represents the area of the garden in square meters.
