Answered

| Linus has 100 ft of fencing to
use in order to enclose a 1200
square foot rectangular pig pen.
The pig pen is adjacent to a
barn so he only needs to form
three sides.
I can determine the
dimensions of the fence,
showing my steps.​

Answer :

lublana

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]

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