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
