SOLUTION: An architect is designing a rectangular family room with a perimeter of 48\m. What dimensions will yield the maximum area? What is the maximum area?

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Question 1188853: An architect is designing a rectangular family room with a perimeter of 48\m. What dimensions will yield the maximum area? What is the maximum area?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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An architect is designing a rectangular family room with a perimeter of 48 m.
What dimensions will yield the maximum area? What is the maximum area?
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A rectangle of the given perimeter P, which has maximum area, is a square with the side length 
one fourth of the perimeter. Its area is   square units.



In the given case, a rectangular family room of the given perimeter of 48 m, which has maximum area,
is a square with the side length of   = 12 m.


Its area is   =  = 144 square meters.

Solved.

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For more details, see the lessons
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
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.



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