Answer:
21.75 m x 21.75 m
Step-by-step explanation:
87 m of fencing
perimeter: [tex]2l+2w=87[/tex]
⇒ [tex]l=\frac{87-2w}{2} [/tex]
area [tex]A=wl[/tex]
⇒ [tex]A=w(\frac{87-2w}{2} )=\frac{87}{2} w-w^2[/tex]
Max area when [tex]\frac{dA}{dw} =0[/tex]
[tex]\frac{dA}{dw} =\frac{87}{2} -2w=0[/tex] ⇒ [tex]w=21.75[/tex]
Therefore,
[tex]2l+2(21.75)=87[/tex] ⇒ [tex]l=21.75[/tex]
So the dimensions are L = 21.75 and W = 21.75
I know that this is a square, but all squares are technically rectangles.
