Answer:
The corresponding dimensions will be "x = 300 & y = 60".
Explanation:
Available fencing = 600 ft
Fencing,
⇒ [tex]5y+x=600[/tex]
⇒ [tex]x=600-5y[/tex]
As we know,
⇒ [tex]Area =xy[/tex]
On substituting the given values, we get
[tex]=(600-5y)y[/tex]
[tex]=600y-5y^2[/tex] ...(equation 1)
On differentiating with respect to y, we get
⇒ [tex]\frac{dA}{dy} =600-10y[/tex]
[tex]0 = 600-10y[/tex]
[tex]600=10y[/tex]
[tex]y=\frac{600}{10}[/tex]
[tex]y=60[/tex]
On putting the values of y in equation 1, we get
⇒ [tex]600(60)-5(60)^2[/tex]
⇒ [tex]600(60)-5(3600)[/tex]
⇒ [tex]36000 - 18000[/tex]
⇒ [tex]18000[/tex]
Dimensions of the rectangular area:
x = 300
y = 60
