To solve this problem, we'll break down the given information and determine what the expression [tex]\((20 - w) \cdot w\)[/tex] represents.
1. Understanding Perimeter and Variables:
- We know the perimeter of the rectangular garden is 40 meters.
- The perimeter [tex]\(P\)[/tex] of a rectangle is given by the formula [tex]\(P = 2L + 2W\)[/tex], where [tex]\(L\)[/tex] is the length and [tex]\(W\)[/tex] is the width of the rectangle.
- From the problem, we have [tex]\(2L + 2W = 40\)[/tex]. Simplifying this, we get:
[tex]\[
L + W = 20
\][/tex]
- Rearranging for [tex]\(L\)[/tex], we have:
[tex]\[
L = 20 - W
\][/tex]
2. Expression Analysis:
- The problem gives us the expression [tex]\((20 - w) \cdot w\)[/tex].
- From our earlier calculation, [tex]\(L = 20 - W\)[/tex]. Thus, we can substitute [tex]\(L\)[/tex] for [tex]\(20 - W\)[/tex].
- So, the expression [tex]\((20 - w) \cdot w\)[/tex] becomes:
[tex]\[
L \cdot W
\][/tex]
- We know that [tex]\(L \cdot W\)[/tex] is the formula for the area of a rectangle.
3. Conclusion:
- Therefore, the expression [tex]\((20 - w) \cdot w\)[/tex] represents the area of the garden in square meters.
So, the correct answer is:
the area of the garden in square meters
