math

posted by .

The number of feared by Pythagoreans, since it lies halfway between the only two integers that can be both the perimeter and the area of the same rectange

  • math -

    Subjects



    Art



    Business



    Computers



    English



    Foreign Languages



    Health



    Home Economics



    Mathematics



    Music



    Physical Education



    Science



    Social Studies







    Features



    Contribute



    Download



    Experts



    Forum



    Job Openings



    Homework Tips



    Libraries.Jiskha



    Link to Us



    Reference



    School Supplies



    Search







    Homework Help Forum: math
    Current Questions | Post a New Question | Answer this Question | Further Reading

    Posted by Ben on Monday, September 24, 2007 at 8:13pm.

    The number of feared by Pythagoreans, since it lies halfway between the only two integers that can be both the perimeter and the area of the same rectange

    Therefore, we can have rectangles with both area and perimeter of 16 and 18.

    The approach to the solution of a problem of this type, where integer answers are sought, is by treating it as a Linear Indeterminate Algebra problem or a Diophantine Problem as follows: Letting x and y be the integer sides of our rectangles, then the area = xy and the perimeter = 2(x+y). Given that xy = 2(x+y) we derive:
    1--xy - 2x - 2y = 0 or
    2--x = 2y/(y-2)
    3--Clearly, both x and 2y/(y-2) must also be integers.
    4--Set x = k from which y then becomes 2k/(k-2).
    5--Assume values of k and compute x and y.
    k...0...1...2...3...4...5....6....7....8....9....10.....50.....100......
    x...-....1...2...3...4...5....6....7....8....9....10.....50....100......
    y...-...inf..inf..6...4...3+..3....2+..2+..2+...2+...2+.....2+......

    Thus 3 and 6, (or 6 and 3), and 4 and 4 are the only possible answers as y never reaches 2 as an integer.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    sin theta = squre roote of 3 over 4 what is the number feared by pythagoreans, since it lies halfway between the only two intergers that can be both the perimeter and the area of the same rectangle Here is a hint. 16 is one of the …
  2. math

    what is the number feared by the pythagoreans I googled "number feared by the Pythagoreans" and checked the 3rd entry. This is what I found on that web site. Find the number feared by Pythagoreans, since it lies halfway between the …
  3. math

    one of the two numbers that can be both the perimeter and the area of the same rectangle I am assuming that you are seeking the two rectangles that have the area equal to the perimeter. A 4 x 4 square has a perimeter and area of 16. …
  4. Algebra 3-4

    What is the number feared by Pythagoreans since it lies halfway between the only two integers that can be both the perimeter and the area of the same rectangle?
  5. math

    The number of feared Pythagoreans
  6. math

    The number of feared Pythagoreans?
  7. math

    The number feared by Pythagoreans, since it lies halfway between the only two integers that can be both the perimeter and the area of the same rectangle?
  8. math

    the number feared by phythagoreans since it ties halfway between the only two integers that can be both the perimeter and the area fo the same triangle
  9. Math

    7. Which of the following is a true statement?
  10. math

    please check this. 1. What is a reasonable distance between two cities?

More Similar Questions