A roll of 640 feet of chicken wire is used to enclose a rectangular vegetable garden.Express the area A of the garden in terms of its length (x)
To express the area A of the garden in terms of its length x, we need to determine the dimensions of the rectangular garden.
Let's assume the length of the garden is x feet.
To enclose the rectangular garden, we need to consider that there are two lengths and two widths of chicken wire required.
The chicken wire required for the lengths is equal to 2 times the length of the garden: 2x feet.
Similarly, the chicken wire needed for the widths is equal to 2 times the width of the garden.
Now, let's calculate the width of the rectangular garden using the given information:
We know that the total amount of chicken wire available is 640 feet. Therefore, the sum of the lengths and widths of the garden must equal 640 feet.
From the information above, we can write the equation:
2x + 2w = 640
Simplifying the equation, we get:
2x + 2w = 640
Dividing both sides by 2, we have:
x + w = 320
Since we know the length of the garden is x feet, the width can be expressed as:
w = 320 - x
The area A of a rectangular garden is equal to the product of its length and width:
A = x * (320 - x)
Thus, the area A of the garden is expressed in terms of its length x as:
A = 320x - x^2