Pythagorean triangle – perimeter is a square and area a cube

 

 

Find a Pythagorean triangle whose perimeter is a square and area a cube
 

 
 

 
 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

4 Responses to Pythagorean triangle – perimeter is a square and area a cube

  1. Paul says:

    Here are a couple

    {144,192,240}, p = 24^2, area = 24^3
    {150,360,390}, p = 30^2, area = 30^3
    {9216,12288,15360}, p = 192^2, area = 384^3
    {9600,23040,24960}, p = 240^2, area = 480^3
    {12960,57600,59040}, p = 360^2, area = 720^3
    {20808,176256,177480}, p = 612^2, area = 1224^3
    {37026,610368,611490}, p = 1122^2, area = 2244^3
    {103680,194400,220320}, p = 720^2, area = 2160^3
    {104976,139968,174960}, p = 648^2, area = 1944^3
    {109350,262440,284310}, p = 810^2, area = 2430^3
    {113256,301158,321750}, p = 858^2, area = 2574^3
    {113400,119070,164430}, p = 630^2, area = 1890^3
    {127008,435456,453600}, p = 1008^2, area = 3024^3
    {158400,784080,799920}, p = 1320^2, area = 3960^3
    {191646,1238328,1253070}, p = 1638^2, area = 4914^3
    {208568,1504926,1519310}, p = 1798^2, area = 5394^3
    {259920,2462400,2476080}, p = 2280^2, area = 6840^3
    {345744,1361367,1404585}, p = 1764^2, area = 6174^3
    {363776,5086368,5099360}, p = 3248^2, area = 9744^3
    {468198,8655336,8667990}, p = 4218^2, area = 12654^3

    Paul

  2. benvitalis says:

    I’ll work on them tomorrow, and post them … It’s getting late for me. I’m going to sleep.

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