Triangle Sides Length: Perimeter 2002, Integers

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To determine the least possible length of a side of a triangle with a perimeter of 2002 and integer side lengths, the triangle inequality must be applied. Specifically, for sides a, b, and c, the third side must be greater than the absolute difference of the other two sides and less than their sum. This means that if two sides are known, the third side can be calculated accordingly. The minimum side length can be derived from the conditions set by the perimeter and the triangle inequality. Ultimately, the least possible length of a side in this scenario is constrained by these mathematical principles.
the4thcafeavenue
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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
 
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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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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