If $\mathbb K$ is a field I would like to find $$\dim \mathbb K[x,y,z]/(xy,xz,yz).$$

I'm starting to study the concept of dimension of rings and I don't know the basic tools and techniques to discover the dimensions of non-trivial rings like this one. I would be very grateful if someone could help me to solve this question which it will open my mind regarding this new subject.

Thanks in advance

**EDIT**

Since I didn't understand Martin's solution, I'm using another strategy, in order to solve this question, I'm trying to find an isomorphism between $\mathbb K[x,y,z]/(xy,xz,yz)$ and a ring which we know its dimension. I didn't find any possible candidate to this isomorphism, I would like to know if it's possible to solve this question using this strategy.