Why do we assume that the right triangle with perimeter 12 is the 3,4,5 triangle?

There could be other possible triangles as well right?

For eg. 2, 4.8, 5.2 triangle

2 + 4.8 + 5.2 = 12

2²+4.8² = 4 + 23.04 = 27.02

5.2² = 27.02

Why do we assume that the right triangle with perimeter 12 is the 3,4,5 triangle?

There could be other possible triangles as well right?

For eg. 2, 4.8, 5.2 triangle

2 + 4.8 + 5.2 = 12

2²+4.8² = 4 + 23.04 = 27.02

5.2² = 27.02

Its just easier to calculate that way but If you can remember the fact that regular polygon maximizes area than you don’t even need to calculate it .

Oh, I didn’t know that. Is there an explanation for it?

Its better if you remember it in a sense of general understanding because its proof deals with some high level math concepts which I personally tend to avoid but if you wanna look at the proof here are some links :

For all regular n-gons :-

https://math.stackexchange.com/questions/868026/given-a-polygon-of-n-sides-why-does-the-regular-one-i-e-all-sides-equal-encl

For triangles :-

https://math.stackexchange.com/questions/592917/simple-proof-that-equilateral-triangles-have-maximum-area

https://www.cut-the-knot.org/triangle/IsoperimetricEquilateral.shtml