Question to math geeks. I need a method of finding rational right triangle side lengths for a given integer triangle area.

Note: not every integer area is possible.

Any hints?

@xpil When there is a solution with rational lengths you can scale it up to a solution with integer lengths. These three numbers a,b,c are Pythagorean triplets which can be found with several methods:

en.wikipedia.org/wiki/Formulas

The scaled² up area is another boundary condition for a and b.

For your problem you have to go this way backwards 😃

(I hope there is no mistake in my thoughts.)

Follow

I think you're on the right track with this one. I have some reasoning now using that: 

@kdkeller @xpil Say we are looking for a triangle T area A and rational sides x,y,z
Let there be a Pythagorean Triple a,b,c and their triangle have area Δ

T exists if such a triple exists that
A=Δs²
x=as, y=bs, z=cs

Where s (scale) must contain the LCM of a,b,c as a factor.

This is still quite new to me, so I can't be too sure about my reasoning. I don't know either if cases outside this can or can't exist.

Sign in to participate in the conversation
Fosstodon

Fosstodon is an English speaking Mastodon instance that is open to anyone who is interested in technology; particularly free & open source software.