Question

The owner of a horse stable wishes to set up 4 rectangular corrals of identical dimensions along the back wall of an existing barn using 200 ft of fencing. The sides of each corral will be attached to the barn, fencing is not needed along the back wall. Find the function that expresses the combined area of 4 corrals each if each corral is x feet long.

Answer 1

Did you make a sketch ?
Even though you didn't say, I will assume that the corrals are joined with common lengths.
let the width of the entire corral (parallel to the barn) be y ft
let each width of corrals be x ft
So we have y + 5x = 200
y = 200 - 5x

Area = xy = x(200-5x) or 200x - 5x^2

The equation will vary depending on your definition of the variables. Mine avoids unnecessary fractions .

BTW, after you maximize the area function, the dimensions of each corral will be 20 by 25, for a maximum area of 2000 for the combined area