Saturday

February 28, 2015

February 28, 2015

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

- math -
**tchrwill**, Tuesday, September 25, 2007 at 1:51pmSubjects

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.

**Answer this Question**

**Related Questions**

math - The number feared by Pythagoreans, since it lies halfway between the only...

Algebra 3-4 - What is the number feared by Pythagoreans since it lies halfway ...

math - what is the number feared by the pythagoreans I googled "number feared by...

math - the number feared by phythagoreans since it ties halfway between the only...

math - sin theta = squre roote of 3 over 4 what is the number feared by ...

math - The number of feared Pythagoreans?

math - The number of feared Pythagoreans

math - one of the two numbers that can be both the perimeter and the area of the...

MATH - TWO INTEGERS ARE DEFINED AS "PARTNERS" IF BOTH OF THEIR PRIME ...

Physics - A battery with voltage drop of 120V is connected in a ciruit ...