The largest possible total area of the four pens is 14,062.5 ft.²
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Diagrams illustrating the situation can be formed adjusting the width of the included diagram illustrating the general situation.
The expression for the total area is A=( 150- (2Y)/5 ) Y
Reasons:
The given parameter are;
Length of fencing available = 750 ft.
Area to be enclosed = Rectangular
Number of included pens with parallel fencing = Four
Let Y represent the width of the area and let X represent the breadth
Therefore, we have;
2·Y + 5·X = 750
Which gives;
X=(750/5)-(2Y/5)=150-(2Y/5)
The area is therefore;
A=Y [150-(2Y/5)] = 150Y-(2Y²/5)
Differentiate with respect to Y and equate to zero
dA/dY = 150- (4Y/5)=0
Y=(150*5)/4 = 187.5
The width of the maximum area, Y = 187.5 ft.
Which gives;
X=150- (2*187.5)/5 = 75
The breadth of the area, X = 75 ft.
The maximum area, = Y × X, which gives;
= 187.5 ft. × 75 ft. = 14,062.5 ft.²
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