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

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SUMMARY

The discussion focuses on solving for the lengths of the sides of four right triangles defined by the relationships between the short leg, longer leg, and hypotenuse, with the short leg 'a' set at 448. Participants concluded that the integer solutions for the triangle sides are (448, 975, 1073, 495, 952, 840) and (840, 3875, 3965, 1364, 3723, 3627). The challenge lies in ensuring all lengths are integers while satisfying the triangle properties.

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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)
 
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Wilmer said:
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.
 
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...
 
Last edited:

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