Triangles: Short Leg-Longer Leg-Hypotenuse a=448

[Wilmer]

4 right triangles; short leg - longer leg - hypotenuse :
a - b - c
d - e - c
d - f - b
a - f - e

HINT: a = 448 (which to my surprise is lowest case)

 

[Sudharaka]

4 right triangles; short leg - longer leg - hypotenuse :
a - b - c
d - e - c
d - f - b
a - f - e

HINT: a = 448 (which to my surprise is lowest case)

Hi Wilmer, :)

So I think the challenge here is to find the lengths of \(a,b,c,d,e\mbox{ and }f\). Isn't? I don't know if there's a unique answer to this question. But it seems to me that,

\[a=3,\,b=4,\,c=5,\,d=1,\,e=\sqrt{24},\,f=\sqrt{15}\]

satisfies all the restrictions that you have imposed.

Kind Regards,
Sudharaka.

 

[Wilmer]

Sorry...all lengths are integers.
Forgot to mention that.

Lowest I could find:
(a, b, c, d, e, f) = (448, 975, 1073, 495, 952, 840)

And next one is: (840,3875,3965,1364,3723,3627).

I was surprised at how few there are...