Question

Pablo wants to build a rectangular pen for the pig he is raising in his agriculture class. Pablo only has 36 feet of fencing. What representative function can be used to model the area of the rectangular pen as a function of the side length, x?

Answer 1

Area of the rectangular pen is:
`18 \,x-x^2`

Explanation:

We need to specify that the perimeter of the rectangular area of side x adds to the amount of fence Pablo has (36 feet). Recall as well that the opposite sides of a rectangle are equal, so if there is a side of length x, there must be another one of this size as well (a total of 2 x in the perimeter),let's assume that the perpendicular sides to x are of length y, then:

Perimeter= 2 x + 2 y = 36

so, 2 (x+y) = 36 then (x+y) = 18

and therefore the side y should be:

y = 18 - x

Now we can write the formula for representing the area of the rectangle (product of both quantities: x * y

`Area=x\,*\,y = x\,(18-x) =18 \,x-x^2`