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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.

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?

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)

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.

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.

You've inspired me to try and learn more about maths.