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Rational Numbers and Right-Angled Triangles

Hi, struggling on understanding a question and have no idea where to begin.

If

\lambda

m

and

n

are positive rational numbers, and

m > n

, then:

\lambda

(

m^2

n^2

2 \lambda mn

and

\lambda

(

m^2

n^2

) are positive rational numbers.

Hence show how to determine any numbers of right-angled triangles (the length of all of whose sides are rational).

Can anyone give the right solution? (Reps given)

Reply 1

rnd

Erebus

A=\lambda(m^2-n^2)

B=2 \lambda mn

and

C=\lambda(m^2+n^2)

are positive rational numbers.

Show that A^2+B^2=C^2 ?

Then for any suitable lambda, m and n you can find A,B and C giving you your triangle.

By the way, quote me to see how I tidied up your latex a little.

Reply 2

Erebus

rnd

Show that A^2+B^2=C^2 ?

Then for any suitable lambda, m and n you can find A,B and C giving you your triangle.

By the way, quote me to see how I tidied up your latex a little.

I quoted you but I can't see how you tidied the lateX :s allow I do admit I have pretty lame lateXing skills.

Yeah that makes sense, I just didn't understand the question at all due to its wording, seems a lot simpler now.

Reply 3

rnd

Erebus

I quoted you but I can't see how you tidied the lateX

Sorry my mistake. That's because I did it in my quote of you which wouldn't appear in your quote of me.

The main thing was that you don't need to put each term in separate latex blocks.

You can do whole expressions like,