Question

Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest area? The diagrams are not to scale.

A. https://study.ashworthcollege.edu/access/content/group/af6e8f9f-40f5-4e73-9bd7-b87e13cc6d33/geometry_exam_1_files/mc020-1.jpg

B. https://study.ashworthcollege.edu/access/content/group/af6e8f9f-40f5-4e73-9bd7-b87e13cc6d33/geometry_exam_1_files/mc020-2.jpg

C. https://study.ashworthcollege.edu/access/content/group/af6e8f9f-40f5-4e73-9bd7-b87e13cc6d33/geometry_exam_1_files/mc020-3.jpg

D. https://study.ashworthcollege.ed

Answer 1

you likely already know that:

Perimeter = 2*length + 2*width; and
Area = length*width

Consider this: if the enclosure didn't HAVE to be a rectangle, what sort of shape would it be if she wanted to maximize the area? Perhaps the rectangle that would maximize area would be the most similar rectangle to this shape? Are there any kinds of "special" rectangles?

If you need more help, I'll be "a-round".


PS - this problem is very easily solved using calculus, if you want to go that route.