# Thread: Concerning the altitude of an equilateral triangle

1. ## 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?

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.

2. ## Re: Concerning the altitude of an equilateral triangle

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?

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?

3. ## 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)

4. ## Re: Concerning the altitude of an equilateral triangle

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.

5. ## 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.