SOLUTION: The area of a rectangle is 84 square inches. Its length and width are both whole numbers. What is the minimun perimeter of the rectangle? What is the maxium perimeter of the

Algebra ->  Equations -> SOLUTION: The area of a rectangle is 84 square inches. Its length and width are both whole numbers. What is the minimun perimeter of the rectangle? What is the maxium perimeter of the      Log On


   



Question 74990: The area of a rectangle is 84 square inches. Its length and width are both whole numbers.
What is the minimun perimeter of the rectangle?
What is the maxium perimeter of the rectangle?
Help please. Not in book.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
The minimum perimeter for a rectangle of any given area is a square whose edge measure would be sqrt%28area%29

Since your answer must be whole numbers, and 84 is not a perfect square; the minimum perimeter dimensions are the factors of 84 that are closest in value to each other...namely 7 and 12.

This makes the minimum perimeter 2%2A7%2B2%2A12 or 38

Similarly, the maximum perimeter dimensions are the factors of 84 that are farthest in value from each other...namely 1 and 84.

This makes the maximum perimeter 2%2A1%2B2%2A84 or 170