The perimeter of a rectangular-shaped garden is 40 meters. Let [tex]$w$[/tex] represent the width of the garden in meters. What does the expression [tex]$(20-w)w$[/tex] represent?

A. the perimeter of half of the garden in meters
B. the area of half of the garden in square meters
C. the perimeter of the garden in meters
D. the area of the garden in square meters



Answer :

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.