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Minimizing Perimeter (Posted on 2015-03-04) Difficulty: 2 of 5
Let ABC be a triangle with integral side lengths such that angle A=3 * angle B. Find the minimum value of its perimeter.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: A triangle that works, may not be minimum (spoiler) | Comment 5 of 15 |
(In reply to A triangle that works, may not be minimum by Jer)

Seeing that Jer found a solution other than a multiple of the one I found (I had found the minimum and the first three of its multiples), I extended the search beyond a perimeter of 100, to 1500. This time only triangles with a gcd(a,b,c) = 1 are shown:


10 8 3    21 3    124.228866327813 41.4096221092709
48 27 35    110 3    100.671929285762 33.5573097619207
132 64 119    315 3    86.8650731155795 28.9550243718598
195 125 112    432 3    110.609692937532 36.869897645844
280 125 279    684 3    77.5257982895014 25.8419327631671
357 343 20    720 3    133.245925791579 44.415308597193
504 343 253    1100 3    114.639632105215 38.2132107017382
510 216 539    1265 3    70.6693929273037 23.5564643091012

Edited on March 4, 2015, 10:29 am
  Posted by Charlie on 2015-03-04 10:17:17

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