Answer:
Length = 400 m
Width = 200 m
Area = 80,000 m2
Step-by-step explanation:
Let's call the length L and the width W. Then, we have that the perimeter will be:
L + 2W = 800.
We want to maximize the area, that is:
A = L*W
so, from the first equation, we have:
L = 800 - 2W
Using this value in the area equation, we have:
A = (800 - 2W)*W = 800W - 2W^2
To find the maximum, we just need to find the vertix of the quadratic equation, and then apply the value to find the area:
W_vertix = -b/2a
Where a and b are coefficients of the quadratic equation (in our case, a = -2 and b = 800)
W_vertix = -800/(-4) = 200 m
A = (800 - 400)*200 = 80000 m2
L = 800 - 2W = 800 - 400 = 400 m
So the dimensions and area are:
Length = 400 m
Width = 200 m
Area = 80,000 m2
