For this case, the first thing we must do is define variables.
We have then:
w: width
l: long
We write the perimeter of the garden:
[tex]P = 2w + 2l = 376
[/tex]
Then, the garden area is:
[tex]A = w * l
[/tex]
Writing the area depending on the width we have:
[tex]A (w) = w * ((1/2) * (376 - 2w))
[/tex]
Rewriting we have:
[tex]A (w) = (1/2) * (376w - 2w ^ 2)
[/tex]
Deriving the area we have:
[tex]A '(w) = (1/2) * (376 - 4w)
[/tex]
We equal zero and clear w:
[tex](1/2) * (376 - 4w) = 0
376 = 4w
w = 376/4
w = 94 feet[/tex]
Then, the length is:
[tex]l = (1/2) * (376 - 2w)
l = (1/2) * (376 - 2 (94))
l = 94 feet[/tex]
Finally, the area is given by:
[tex]A = w * l
A = 94 * 94
A = 8836 feet ^ 2[/tex]
Answer:
94 * 94; 8836
option 3
