Answer :
Answer:
[tex]20 ft\times 60 ft[/tex] or [tex]30ft\times 40ft[/tex]
Step-by-step explanation:
We are given that
Total fencing used=100 ft
Area enclosed=1200 square ft
Let length of rectangular pig pen=x
Breadth of rectangular pig pen=y
Fencing used=2x+y
[tex]100=2x+y[/tex]
[tex]y=100-2x[/tex]
Area of rectangular pig pen=[tex]xy=x(100-2x)[/tex]
[tex]1200=100x-2x^2[/tex]
[tex]2x^2-100x+1200=0[/tex]
[tex]x^2-50x+600=0[/tex]
[tex]x^2-20x-30x+600=0[/tex]
[tex]x(x-20)-30(x-20)=0[/tex]
[tex](x-20)(x-30)=0[/tex]
[tex]x=20[/tex]
[tex]x-30=0\implies x=30[/tex]
When x=20ft
[tex]y=100-2(20)=60[/tex]ft
When x=30 ft
[tex]y=100-2(30)=40[/tex]ft
Dimension of fence is give by
[tex]20 ft\times 60 ft[/tex] or [tex]30ft\times 40ft[/tex]