SOLUTION: If the area is 64 square feet what is the smallest perimeter

Question 476600: If the area is 64 square feet what is the smallest perimeter
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The area of a rectangle is given by:

so we can say:

The perimeter is given by:

Substituting we can write a function for the perimeter in terms of

Extremum where the first derivative is equal to zero:

But discard the negative root, hence:

The extremum is a minimum if the second derivative is positive at the extreme point.

Since

and

are both positive quantities, the second derivative is positive for all values of

and therefore the extremum is a minimum.

Take the positive square root of your given area and you have your answer.

John

My calculator said it, I believe it, that settles it

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