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Cut Wire (Posted on 2005-05-20) Difficulty: 3 of 5
A piece of wire is to be cut into two pieces (one bent into the shape of a regular p-gon and the other a regular q-gon).

If

1) p = 2*q,
2) 2*perimeter(q-gon) = 3*perimeter(p-gon), and
3) the sum of the two areas is minimized;

then what is the value of q?

See The Solution Submitted by Bractals    
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Hints/Tips Jer & Charlie | Comment 3 of 6 |
 
I think you both are misinterpreting the problem
(which is probably my problem).
 
We have three restrictions:
1) p = 2*q
2) 2*Perimeter(q-gon) = 3*Perimeter(p-gon)
3) the sum of the areas is minimized
For each (p,q) pair (6,3), (8,4), (10,5), ...
I can cut the wire such that
A) Neither 2) nor 3) is satisfied,
B) 2) is satisfied, but not 3),
C) 3) is satisfied, but not 2),
D) Both 2) and 3) are satisfied.
I want the pair or pairs where 2) and 3)
are satisfied.
I do not want the pair that minimizes the
sum of the areas for all pairs.
 

  Posted by Bractals on 2005-05-20 21:01:59
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