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

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

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

So we get

Substituting the value of y, we will get

Second part

The area is maximum at the vertex, and vertex is

And

And that's the required dimensions .

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180