Question

A farmer wants to build a fence along a river. he has 900 feet of fencing and wants to enclose a rectangular pen on three sides (with the river providing the fourth side). if x is the length of the side perpendicular to the river, determine the area a of the pen as a function of x.

Answer 1

The first thing we must do is define variables.

We have then:

x: the length of the side perpendicular to the river

y: the length of the side parallel to the river

The area of the rectangle is given by:

`A = x * y`

On the other hand, the perimeter of the rectangle is:

`2x + y = 900`

From here, we clear the value of y:

`y = 900-2x`

Then, rewriting the area we have:

`A (x) = x * (900-2x)`

`A (x) = 900x-2x ^ 2`

`A (x) = - 2x ^ 2 + 900x`

Answer:

the area of the pen as a function of x is:

`A (x) = - 2x ^ 2 + 900x`