Question

| 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 1

`20 ft* 60 ft` or
`30ft* 40ft`

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

`100=2x+y`

`y=100-2x`

Area of rectangular pig pen=
`xy=x(100-2x)`

`1200=100x-2x^2`

`2x^2-100x+1200=0`

`x^2-50x+600=0`

`x^2-20x-30x+600=0`

`x(x-20)-30(x-20)=0`

`(x-20)(x-30)=0`

`x=20`

`x-30=0\implies x=30`

When x=20ft

`y=100-2(20)=60`ft

When x=30 ft

`y=100-2(30)=40`ft

Dimension of fence is give by

`20 ft* 60 ft` or
`30ft* 40ft`