The largest possible total area of the four pens is 285610 ft²
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the length of the pen and x represent the width of the pen.
Hence:
Perimeter = x + y + x + y + x + x + x = 2y + 5x
2y + 5x = 3380
y = (3380 - 5x)/2 (2)
Area (A) = xy
A = x * (3380 - 5x)/2
A = (3380x - 5x²)/2
The maximum area is at A' = 0, hence:
A' = (1/2)(3380 - 10x)
0 = (1/2)(3380 - 10x)
10x = 3380
x = 338 ft.
2y + 5(338) = 3380
y = 845 ft.
Largest possible total area = 338 * 845 = 285610 ft²
The largest possible total area of the four pens is 285610 ft²
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