A rectangular plot of ground containing 432 ft is to be fenced within a large lot. Express the perimeter of the plot as a function of the width. What is the domain of this function?

Question

I am honestly so confused on how to work this out.

Answer 1

Maisie

I will model this using 500 ft (think it should be 500 ft² as it is an area).

Draw a rectangle. Suppose the width of the rectangle is x. Then if y is the length of the rectangle, then

the area of the rectangle will be xy, and the perimeter will be x + x + y + y = 2x + 2y.

So we know xy = 500, so y = 500/x

So if P is the perimeter P = 2x + 2y = 2x + (1000/x)

So here - you need to adjust this , so that the area is 432 not 500.

Then you need to find the domain of P.

Mike