Answer:
65 ft by 39 ft
Step-by-step explanation:
Let x ft be the length of each part and y ft be the width of each part. The total perimeter of all 5 parts is
[tex]6x+10y=780[/tex]
The length of the large rectangle is 5y ft and the width of the large rectangle is x, so the total area is
[tex]A=x\cdot 5y[/tex]
From the first equation,
[tex]y=78-0.6x[/tex]
Substitute it into the area expression:
[tex]A(x)=x\cdot 5(78-0.6x)=390x-3x^2[/tex]
Find the derivative:
[tex]A'(x)=390-3\cdot 2x=390-6x[/tex]
Equate it to 0:
[tex]390-6x=0\\ \\6x=390\\ \\x=65[/tex]
Then
[tex]y=78-0.6\cdot 65=78-39=39[/tex]
