Question

A horticulturalist is building a fence around a rectangular garden using the side of the building for one side of the enclosure. she has 81 feet fencing. what should be the dimensions of the enclosure be so that she can maximize the garden's area?

Answer 1

If the dimensions of the garden are x and y, with the building along side x, then

x+2y = 81
So, the area (xy) is

(81-2y)y = 81y - 2y^2
This is a parabola, with vertex at y=20.25

Now you can figure the other dimension.

I suspect you meant to say 80 ft of fencing, but only you can decide that.

Answer 2

;kn;n