Beyond Pythagoras

                13=13x13=169

Therefor

And the numbers 7,24 and 25 satisfy the condition too;

                7+24=25

Because        7=7x7=49

                24=24x24=576

                25=25x25=625

Therefor

The units 5,12 and 13 can be lengths-in appropriate units-of a right-angled triangle

The Perimeter = 5+12+13= 30 units

The Area x5x12= 30 units

The units 7,24 and 25 can also be length in appropriate units-of a right-angled triangle

The Perimeter = 7+24+25= 46 units

And the Area = x7x24= 84

There are relatively easy patterns to work out; the length of the shortest side, the length of the middle side and the length of the longest side but not to the perimeter or the area.  The shortest length pattern is 2n+1, the pattern equation for the middle length is 2n2+2n and the pattern equation for the longest side is 2n2+2n+1.  At first I thought it would not be possible to create an equation for the perimeter and the area but then I realised that the equation for the perimeter would first be all of the other equation added up.  This means that (2n+1)+(2n2+2n)+(2n2+2n)+(2n2+2n+1) is the paremeter and (2n+1)(2n2+2n)

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