2 Pythagorean triangles – sum/difference of perimeters,difference of areas are squares

 
 

Find two Pythagorean triangles the sum or difference of whose perimeters is a square,
the difference of areas a square

 

 
 

 
 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to 2 Pythagorean triangles – sum/difference of perimeters,difference of areas are squares

  1. Paul says:

    As there area quite a few of each type, this list is where both the sum and difference of the perimeters and difference of area are squares.

    Format is {{a, b, c}, {d, e, f}} or in short terms {{A}, {B}}
    {perimeter B – perimeter A = n^2
    {perimeter B + perimeter A = m^2
    {area B – area A = o^2

    {{16,63,65},{30,72,78}}
    180 – 144 = 6^2
    180 + 144 = 18^2
    1080 – 504 = 24^2

    {{24,32,40},{32,60,68}}
    160 – 96 = 8^2
    160 + 96 = 16^2
    960 – 384 = 24^2

    {{54,72,90},{72,135,153}}
    360 – 216 = 12^2
    360 + 216 = 24^2
    4860 – 1944 = 54^2

    {{64,252,260},{120,288,312}}
    720 – 576 = 12^2
    720 + 576 = 36^2
    17280 – 8064 = 96^2

    {{96,128,160},{128,240,272}}
    640 – 384 = 16^2
    640 + 384 = 32^2
    15360 – 6144 = 96^2

    {{96,2303,2305},{98,2400,2402}}
    4900 – 4704 = 14^2
    4900 + 4704 = 98^2
    117600 – 110544 = 84^2

    {{150,200,250},{200,375,425}}
    1000 – 600 = 20^2
    1000 + 600 = 40^2
    37500 – 15000 = 150^2

    Paul.

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