SOLUTION: find the dimensions and maximum area of a rectangle if its perimeter is 40 centimeters Pls help I need it

Question 1180587: find the dimensions and maximum area of a rectangle if its perimeter is 40 centimeters
Pls help I need it
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

If the length = and the width = then the perimeter

→
→
As for the area A
.........substitute

And we have to find an extreme for that
'= by setting the derivative to =

then
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the perimeter is 40 centimeters.
the perimeter is equal to 2L + 2W.
L = length
W = width.
when L = W, you can replace L with W or W with L to get:
perimeter = 4L or 4W.
formula for perimeter becomes 4L = 40 or 4W = 40.
this makes L = 10 and W = 10.
the area is L * W = 10^2 = 100
that should be the maximum area since the maximum area of a rectangle is when the rectangle is a square.
to confirm, you can try any other combination of 2L + 2W = 40 and then find the area.
the possible combinations are shown below:
you can see that the maximum area is when L = W.

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