Answer:
41 ft wide and 61.5 ft long
Step-by-step explanation:
Let
Width = x ft
Length = y ft
Total fencing = 3 Width + 2 Lenght
So,
[tex]3x+2y=246\\ \\2y=246-3x\\ \\y=123-1.5x[/tex]
Find the area:
[tex]A(x)=x\times y\\ \\=x(123-1.5x)\\ \\=123x-1.5x^2[/tex]
Find the derivative:
[tex]A'(x)=123-2\cdot 1.5x=123-3x[/tex]
Equate it to 0:
[tex]123-3x=0\\ \\3x=123\\ \\x=41\ ft\\ \\y=123-1.5\cdot 41=61.5\ ft[/tex]
