Answer:
the dimensions of the garden that would give max area would be
W (width) = 15 ft and L (length) = 30 ft.
Step-by-step explanation:
Let the length of the garden be L and the width W.
Then L*W must equal 400 ft^2.
The perimeter involving 3 sides is then P = 60 ft = 2W + L, and this can be solved for L: L = 60 ft - 2W. Subbing 60 ft - 2W into the previous equation, we get:
(60 ft - 2W)(W) = 400 ft^2, or
-2W^2 + 60W - 400 = 0,
which can be reduced to:
-W^2 + 30W - 200 = 0
We want to find the max area, that is, the max of the function
-W^2 + 30W - 200 = 0
Using the formula x = -b/2a for x-coordinate of vertex, we get:
30
W = - ---------- = 15
2(-1)
Thus, the dimensions of the garden that would give max area would be
W (width) = 15 ft and L (length) = 30 ft.
