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

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) (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 and .

If , you have a square, otherwise it is a rectangle.
The perimeter will be --> -->
The area will be
We have area as a function of x.
We can write it as

It is a quadratic function, that can be graphed as a parabola.
Like all quadratic functions
(in general written as )
with a negative leading coefficient,
has a maximum at .
In this case, that leading coefficient is ,
the number multiplying .
The coefficient of the term in is ,
and the maximum is at -->
The maximum occurs at
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