Operator overloading ==, !=, Equals

As Selman22 said, you are overriding the default object.Equals method, which accepts an object obj and not a safe compile time type.

In order for that to happen, make your type implement IEquatable<Box>:

public class Box : IEquatable<Box>
{
    double height, length, breadth;

    public static bool operator ==(Box obj1, Box obj2)
    {
        if (ReferenceEquals(obj1, obj2))
        {
            return true;
        }
        if (ReferenceEquals(obj1, null))
        {
            return false;
        }
        if (ReferenceEquals(obj2, null))
        {
            return false;
        }

        return obj1.Equals(obj2);
    }

    public static bool operator !=(Box obj1, Box obj2)
    {
        return !(obj1 == obj2);
    }

    public bool Equals(Box other)
    {
        if (ReferenceEquals(other, null))
        {
            return false;
        }
        if (ReferenceEquals(this, other))
        {
            return true;
        }

        return height.Equals(other.height) 
               && length.Equals(other.length) 
               && breadth.Equals(other.breadth);
    }

    public override bool Equals(object obj)
    {
        return Equals(obj as Box);
    }

    public override int GetHashCode()
    {
        unchecked
        {
            int hashCode = height.GetHashCode();
            hashCode = (hashCode * 397) ^ length.GetHashCode();
            hashCode = (hashCode * 397) ^ breadth.GetHashCode();
            return hashCode;
        }
    }
}

Another thing to note is that you are making a floating point comparison using the equality operator and you might experience a loss of precision.