SOLUTION: he perimeter of a rectangle is 48 cm. Find the lengths of the sides of the rectangle giving the maximum area. Enter the answers for the lengths of the sides in increasing order.

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Question 1069393: he perimeter of a rectangle is 48 cm. Find the lengths of the sides of the rectangle giving the maximum area.
Enter the answers for the lengths of the sides in increasing order.
so what I did is 48=2x+2y
2y=48-2x
y=(48-2x)/2
y= 24-x
then I did
a=xy
a=x(24-x)
a=24x-x^2
I am very stuck and unsure if im even working the problem out correctly

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!

Area A is a function of either x or y, and the perimeter equation can be simplified.

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No need to try multiplying the quadratic expression. This is a parabola function and it has vertex as a maximum.

Roots or zeros?
x=0 or x=24.

The maximum occurs in the exact middle between the roots.

A will have its maximum, the vertex, at x=12.

Dimensions will be 12, and 24-x=24-12=12;
meaning the shape will be a square.

Maximum area will be .
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THE SHAPE FOR THE MAXIMUM AREA OF A RECTANGLE IS A SQUARE.

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
A rectangle with a given perimeter which has the maximal area is a square.

If you know it, you will find the answer to your problem in one line:

        the side = = 12.

The full coverage of this topic see in 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 online textbook under the topic
"Finding minimum/maximum of quadratic functions".