SOLUTION: If we want to enclose the largest possible rectangle or square with a perimeter of 16 cm, what will its dimensions be ?

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Question 633890: If we want to enclose the largest possible rectangle or square with a perimeter of 16 cm, what will its dimensions be ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It will be a 4 cm by 4 cm square.

Let the length of adjacent sides be x and y.

If x=y, you have a square, otherwise it is a rectangle.
The perimeter will be x%2By%2Bx%2By=2%28x%2By%29=16 --> x%2By=8 --> y=8-x
The area will be A=x%2Ay=x%288-x%29=8x-x%5E2
We have area as a function of x.
We can write it as
A%28x%29=-x%5E2%2B8x
It is a quadratic function, that can be graphed as a parabola.
Like all quadratic functions
(in general written as f%28x%29=ax%5E2%2Bbx%2Bc)
with a negative leading coefficient,
A%28x%29 has a maximum at x=-b%2F2a.
In this case, that leading coefficient is a=-1,
the number multiplying x%5E2.
The coefficient of the term in x is b=8,
and the maximum is at x=-8%2F2%2F%28-1%29 --> highlight%28x=4%29
The maximum occurs at