Triangle Sides Length: Perimeter 2002, Integers

  • Context: High School 
  • Thread starter Thread starter the4thcafeavenue
  • Start date Start date
Click For Summary
SUMMARY

The minimum possible length of a side of a triangle with a perimeter of 2002 and integral side lengths is established through the triangle inequality theorem. Given sides a, b, and c, the conditions dictate that the third side must be greater than the absolute difference of the other two sides and less than their sum. For a triangle with a perimeter of 2002, the smallest integer side length is 1, while the other two sides must be adjusted accordingly to maintain the perimeter and satisfy the triangle inequality.

PREREQUISITES
  • Understanding of the triangle inequality theorem
  • Basic knowledge of integer properties
  • Familiarity with perimeter calculations
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the triangle inequality theorem in depth
  • Explore integer programming techniques for geometric problems
  • Learn about perimeter optimization in triangle configurations
  • Investigate examples of integral side lengths in various triangle types
USEFUL FOR

Mathematicians, geometry enthusiasts, students studying triangle properties, and anyone interested in integer-based geometric problems.

the4thcafeavenue
Messages
14
Reaction score
0
ok here goes: what is the lesat possible length of a side of a triangle whose perimeter is 2002 and whose sides have integral (integer) lengths?

major help is needeeeedddd
 
Mathematics news on Phys.org
Here is a hint...Given two sides of a triangle, the third must always be greater than the difference, but less than the sum

example: triangle with sides a, b, and c...a=3, b=4
c must be greater than 1, but less than 7
 

Similar threads

High School Find triangles with areas that are integers
  • · Replies 20 ·
Replies
20
Views
5K
High School Understanding the Pythagorean Theorem
  • · Replies 38 ·
2
Replies
38
Views
7K
MHB Is there a formula for finding the perimeter of a triangle with known vertices?
  • · Replies 3 ·
Replies
3
Views
2K
Sides of a triangle
  • · Replies 16 ·
Replies
16
Views
3K
MHB Integer-Sided Right Triangle: 2001 Leg Length & Minimum Other Leg Length
  • · Replies 2 ·
Replies
2
Views
2K
MHB Are the coordinates of the vertices of this triangle all integers?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Can an Ellipse Help Solve the Scalene Triangle Problem?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Infinite Isosceles Triangles w/ Integer Sides & Areas
  • · Replies 2 ·
Replies
2
Views
2K
High School A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Integer Cevians - Equilateral Triangles
  • · Replies 2 ·
Replies
2
Views
2K