ye has 44 feet of fencing to enclose a rectangular garden. She wants to to enclose as much area as possible. use trial and error to find maximur are faye can enclose with all 44 feet of fence. name the lencth and width that gives maximum area.
length + width = 22
w = 22-L
A = w L = (22-L)L
A = 22 L - L^2
that is a parabola, find the vertex
L^2 - 22 L = -A
L^2 - 22 L + 121 = -A+121
(L-11)^2 = -A + 121
vertex (maximum of A) at L = 11, A = 121
then w also = 11
and it is a SQUARE :)
safa
To find the dimensions that will give maximum area, you can use trial and error by considering different combinations of length and width and calculating the corresponding areas. Let's start with the given information.
Faye has 44 feet of fencing, and she wants to enclose a rectangular garden. Let's assume the length of the rectangular garden is "L," and the width is "W." According to the problem, the perimeter of the garden should be equal to 44 feet. Using this information, we can set up the equation:
2L + 2W = 44
Simplifying this equation, we have:
L + W = 22
Now, let's create a table to calculate the area for different combinations of length and width:
Length (L) | Width (W) | Area (A)
--------------------------------
1 | 21 | 21
2 | 20 | 40
3 | 19 | 57
4 | 18 | 72
... | ... | ...
21 | 1 | 21
By going through this table and calculating the area for each combination, we can see that as the length increases, the width decreases, and vice versa. We are looking for the combination that gives us the highest possible area.
From the table, we can observe that when L = 11 and W = 11, the total area is 11 * 11 = 121, which is the maximum area we can achieve with the given amount of fencing.
So, the dimensions that give the maximum area are:
Length = 11 feet
Width = 11 feet
Area = 121 square feet