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:
[tex] A = x * y [/tex]
On the other hand, the perimeter of the rectangle is:
[tex] 2x + y = 900 [/tex]
From here, we clear the value of y:
[tex] y = 900-2x [/tex]
Then, rewriting the area we have:
[tex] A (x) = x * (900-2x) [/tex]
[tex] A (x) = 900x-2x ^ 2 [/tex]
[tex] A (x) = - 2x ^ 2 + 900x [/tex]
Answer:
the area of the pen as a function of x is:
[tex] A (x) = - 2x ^ 2 + 900x [/tex]
