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

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

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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

what are your parametric solutions?

No parametric solutions, I just generated the PT’s and tested for square perimeter and cubic area.

P

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