SOLUTION: Find the maxumum area of a rectangle whose perimeter is 32

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Question 1184730: Find the maxumum area of a rectangle whose perimeter is 32
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
common enough exercise which can be found and solved in many sources.

This one, maximum area is 64=8%5E2 square units.

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.

When the perimeter of a rectangle is given, the maximum area has a square
with the side length one fourth of the given perimeter.

This fact is very well known.

You can read about it (with the proof) from the lesson
    - A rectangle with a given perimeter which has the maximal area is a square
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


In your case,  the maximum area is   %2832%2F4%29%5E2 = 8%5E2 = 64   square units.