How do I find A(x) ?

Question

A rancher has 200 feet of fencing to enclose two adjacent rectangular Corrals.

Write the total area A of the Corrals as a function of x

Answer 1

Call the length of the adjacent side of each corral x, and the other side y.

The area of each corral is x*y, so the total area is A = 2xy.

The total perimeter is 3x + 4y = 200 since the corrals share one side with length x (a drawing is helpful).

Solving for y:

3x + 4y = 200

y = (200 - 3x) / 4

y = 50 - 0.75x

Now substitute this equation for y into A to find the equation A(x).

A = 2xy

A = 2x(50-0.75x)