SOLUTION: Not sure if "topic": selection is correct. how do you figure out the smallest and largest possible perimeters of an area: i.e. (1) A picture frame has an area of 48 sq inche

Question 965124: Not sure if "topic": selection is correct.
how do you figure out the smallest and largest possible perimeters of an area:
i.e. (1) A picture frame has an area of 48 sq inches. What is the largest possible perimeter of the pic frame? (2) A backyard has an area of 64 sq feet. What is the smallest possible perimeter of the backyard?

Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
how do you figure out the smallest and largest possible perimeters of an area:
i.e. (1) A picture frame has an area of 48 sq inches. What is the largest possible perimeter of the pic frame?
There is no largest perimeter. It can be 1 by 48 --> 98
Or 0.01 by 4800 --> 9600.02
Or 0.0001 by 480000, etc
--------------------
(2) A backyard has an area of 64 sq feet. What is the smallest possible perimeter of the backyard?
Minimum for a rectangle is a square, 8 by 8 --> 32 ft.
A circle is the minimum, solve for r, then for C.

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Question 1 is a rectangular shape that can be analyzed. Question 2 shape is unspecified so is incomplete.

x and y dimensions of the rectangle.
p for perimeter:
and
-

The only method for minimizing or maximizing the perimeter seems to be derivatives.

Finding extreme values, set derivative to zero. Continue other steps.

Denominator cannot be zero, and for derivative be zero, the NUMERATOR must be equated to zero.

, the positive value only.
-

-
and from the original area equation, obviously , making the area shape as a SQUARE shape. The values for MINIMUM perimeter.

Note that you will find this is for MAXIMUM area. Check about the area equation and you should find no minimum.

Here is a graph for the PERIMETER equation, in one or either variable, here being , which shows a MINIMUM for the perimeter:

RELATED QUESTIONS
The problem states, Of all possible quotients of the numbers 10, -1/2, -5, and 1/5, which (answered by stanbon)
Hi. I can't figure out how to solve this problem. At first I solved for L=250-W and then... (answered by josgarithmetic)
Hello, I am in need of help. I have this problem on an optional assignment, and I cannot... (answered by macston)
I am not sure that I chose the correct topic for the question. It is algebriac, but I am... (answered by mananth)
Hello, Can someone please explain how I can determine the number of permutation for the... (answered by scott8148)
Hello i need help. im not sure if i out it under the right topic i have 3 problems i do... (answered by richwmiller)
how do I figure out the largest possible product of two even integers whose sum is... (answered by ikleyn)
I'm not sure if this is in the correct section, but I really need help as soon as... (answered by reviewermath)