SOLUTION: what is the geatest possible area of a rectangle if its perimeter is 30 cm

Question 214015: what is the geatest possible area of a rectangle if its perimeter is 30 cm

Found 3 solutions by rfer, drj, josmiceli:
Answer by rfer(16322)   (Show Source): You can put this solution on YOUR website!
A square is the largest area
A=7.5*7.5
A=56.25 sq cm
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
What is the greatest possible area of a rectangle if its perimeter is 30 cm.

The greatest possible area is when the sides are equal or a square and the perimeter is adding up the lengths of all four sides in this case.

So let s be the side of the square.

Then Perimeter P=4s or s=P/4=30/4=7.5 cm.

The Area or 56.25 square centimeters.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
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Good luck in your studies!

Respectfully,
Dr J

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
If the sides are and ,
then

The - sign tells me this is a parabola with
a peak at the top, or a maximum
The maximum occurs exactly between the
roots, or at }

and

A 7.5 x 7.5 rectangle, or a square, has the max area
which is cm2
You can prove this by changing the square slightly
and keep the perimeter the same, say
7.4 x 7.6
perimeter =

(just a little smaller than 56.25)

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