(C#) Enemy health and take damage from bullets

I just need a clearing on what im doing. Im going to have Heath on my Enemy and its going to take damage from my bullets and when health is <= 0. So far, i have an empty script i calld EnemyHeathScript, where i put

public class EnemyHealth : MonoBehaviour {

public int EnemyMaxHealth = 100;
public int EnemyCurHealth = 100;

Thats it so far. And on my bullet script i have

public class DestroyScript : MonoBehaviour {

public float lifetime = 1.0f;
void Start ()		
{
}
void Update () {
}
void Awake ()
{
	Destroy (gameObject,lifetime);
}
void OnTriggerEnter(Collider other)
{
	if(other.gameObject.tag == "Enemy")
	{
	
		DestroyObject(other.gameObject);
		Destroy(gameObject);
	}
}

Not sure what to add on the bullet script and i want to know how to set up my EnemyHealthScrip so it takes damage. I know it isent that hard, but i want to be on the safe side!

Should be something like this:

 if(other.gameObject.tag == "Enemy")
    {
       other.gameObject.GetComponent<name of enemy health script>().EnemyCurHealth = EnemyCurHealth - damage;
       DestroyObject(other.gameObject);
       Destroy(gameObject);
    }

And you might want to change it so destroying the enemy only happens when EnemyCurHealth<=0.