# Concerning the altitude of an equilateral triangle

• Aug 21st 2011, 02:33 PM
blis
Concerning the altitude of an equilateral triangle
I appologise if this is the wrong forum. I figured triangles are trigonometry.

Are there any equilateral triangles where both h and a are integers?
Attachment 22107
I found this formula on the internet.

h = (1/2) * √3 * a

Is there any way to re-arrange it to get rid of the square root?

I'm trying to write a program to answer my original question but it would round off a value for the square root which would make it impossible to find a match. Sorry if this is really basic, I left school a long time ago.
• Aug 21st 2011, 02:37 PM
Plato
Re: Concerning the altitude of an equilateral triangle
Quote:

Originally Posted by blis
I appologise if this is the wrong forum. I figured triangles are trigonometry.
Are there any equilateral triangles where both h and a are integers?
Attachment 22107
I found this formula on the internet.
h = (1/2) * √3 * a
Is there any way to re-arrange it to get rid of the square root?

$\displaystyle \frac{4h^2}{a^2}=3$

But that is no better. Is it?
• Aug 21st 2011, 02:59 PM
blis
Re: Concerning the altitude of an equilateral triangle
I think that will work actually. Thank you.

I can get it to keep trying different integers for a and h until it equals 3(if ever)
• Aug 21st 2011, 03:18 PM
Plato
Re: Concerning the altitude of an equilateral triangle
Quote:

Originally Posted by blis
I can get it to keep trying different integers for a and h until it equals 3(if ever)

Let this be a lesson to everyone.
Always post what you mean to ask in the first place.

You never find integer solutions for a & h.

In order for $\displaystyle \frac{4h^2}{a^2}=3$ we must have $\displaystyle a=2\cdot 3^j~\&~h=3^k$.

In effect, $\displaystyle 3^{2k-2j}=3$. But that is impossible.
• Aug 22nd 2011, 01:16 AM
blis
Re: Concerning the altitude of an equilateral triangle
Most of that goes over my head but to hear that it is indeed impossible saves me a lot of time.

Thanks.