Question

Hilda has a rectangular garden by the river in front of her house. The area she uses for planting tomatoes is three times as large as that she uses for beets. If she has 270 yards of fencing material to enclose the garden to protect it fro, rodents, will the total area attain a maximum, or, a minimum value? What would be the dimensions, and the value of the corresponding area?

Answer 1

of course the are will be minimum if the width of length is zero. But that's not what you want, I'm sure.

So, you want the arrangement of fences which will produce the maximum area.

You don't say how the area is to be divided. Is the beet garden enclosed by the tomatoes, or are the two separate enclosures, or are they two rectangles sharing a boundary? Do the beets sit in one corner of the tomato field? Is it just one large rectangle, with beets and tomatoes sharing the space? Each way gives a different answer.

Answer 2

Yes, there are two rectangles sharing a boundary.

|Tomatoes | Beets |

Thank you.

Answer 3

Area for Tomatoes = 3x (Area for Beets)