Question

Fencing a horse corral carol has 2400 ft of fencing to fence in a rectangular horse corral. (a) find a function that models the area of the corral in terms of the width x of the corral. (b) find the dimensions of the rectangle that maximize the area of the corral

Answer 1

Here it is given that the width is x ft and total length of the fence is 2400 ft .

Let the length be y ft

So we have

$2(x+y) =2400 \\ x+y=1200 \\ y = 1200 -x$

Let A represents area, and area is the product of length and width .

So we get

$A = x y$

Substituting the value of y, we will get

$A = x (1200-x)= 1200x -x^2$

Second part

The area is maximum at the vertex, and vertex is

$x = - \frac{1200}{2(-1)} = 600 feet$

And

$y=1200-x = 1200-600 = 600 feet$

And that's the required dimensions .