Answer:
A = (800 yd - x)x, [0, 800]
Step-by-step explanation:
The farmer fences in this rectangular garden using 1600 yds of fencing. Using the formula for the perimeter of a rectangle,
P = 2x + 2L, where x is the width and L is the length. Here P = 1600 yd.
Solving for L: 1600 yd = 2x + 2(L) → 800 yd = x + L → L = 800 yd - x.
The area of the rectangle is A = L·x. Subbing (800 yd - x) for L, we get:
A = (800 yd - x)x. This is the desired formula for the area of the rectangle as a function of x alone. Neither length nor width can be negative, so the domain of this function A is x ≤ 800 yd.
Let the length of the rectangular garden = l yards
And the width of the garden = w yards
Farmer has the fence in length = 1600 yards to cover all the sides of the garden
Therefore, Perimeter of the rectangular garden = 1600 yards
Since, perimeter of the rectangular garden is given by the expression,
Perimeter = 2(l + w)
By substituting the values in the expression,
1600 = 2(l + x)
l + x = 800
l = 800 - x -------(1)
Since, area of the rectangle = Length × Width
= l × w
= lx
Therefore, by substituting the value of 'l' in terms of 'x' in from equation (1),
Area of the rectangular garden = (800 - x)x
If the area of the garden is represented by by the function A(x),
A(x) = (800 - x)x
A(x) = 800x - x²
Since, Area can not be negative or zero,
Domain of the function will be 0 < x < 800
Learn more,
https://brainly.com/question/4537844
