## Pythagorean triangle (a,b,c) such that Area + (a+b)^2 is a square

(78320,   190281,   205769)   is a primitive Pythagorean triangle
Perimeter = 474370
Area = 7451403960

If in the Pythagorean triangle   (78320, 190281, 205769)   we add the area to the square of the sum of the legs,   we get a square:

$7451403960 \; + \; (78320 + 190281)^2 \; = \; 282131^2$

Find other examples.

math grad - Interest: Number theory
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### One Response to Pythagorean triangle (a,b,c) such that Area + (a+b)^2 is a square

1. Paul says:

Here are a few more examples

{156640,380562,411538,29805615840} , 29805615840 + (156640 + 380562)^2 = 564262^2
{234960,570843,617307,67062635640} , 67062635640 + (234960 + 570843)^2 = 846393^2

Paul.