SOLUTION: Of all rectangles with a perimeter of 34, which one has the maximum  area?  (Give the  dimensions.) The rectangle that has the maximum area has length 

Algebra ->  Test -> SOLUTION: Of all rectangles with a perimeter of 34, which one has the maximum  area?  (Give the  dimensions.) The rectangle that has the maximum area has length       Log On


   

Question 1156757: Of all rectangles with a perimeter of 34, which one has the maximum  area?
 (Give the  dimensions.)
The rectangle that has the maximum area has length  ? and width ? .
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
.

Such a rectangle is a square with the side length  34%2F4 = 82%2F4 = 81%2F2 = 8.5 units.

Ignore the answer   " 91%2F2 "   from @josgarithmetic, since it is INCORRECT.

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This subject and this question are very popular. 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.

They explain in details, why it is so. Every middle school student should know it.

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.