How to connect a cisco router to another cisco router

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I understand if two office are far away (eg. New York - California) apart you can use the internet to communicate using the routers but (with out internet) if Company ABC started with 20 users and all of them were in one building, during the years it grew from 20 to 110 employees and now the company is using two building distance less than 1,000 feet. They are using fiber optic to connect from one building to the other and each building has it own server one primary the other secondary. In case the primary fail (Hardware) the secondary take over using heartbeat technology.

My questions are:
1)What is the benefit having two sub net ( or more) ?

2)If you want to have more than one sub net and the router are far away between 150 to 900 feet, what type of interface you will use to connect the router(see example ablove)

thanks

Dale,
For the first question, you're scenario sets this up very nicely for the use of multiple subnets. If the company has grown over time, it's like to grow again and likely to need multiple departments too. Creating multiple subnets will help segregate traffic according to your business need (e.g. HR Dept traffic separate from the Marketing Dept). Also for future scalability, if the business continues to grow with one network (such as a 192.168.1.0/24) you'll still need another network. Let's say you pick a 172.16.1.0/24 next. This will work but you'll not be able to take advantage of things like route summarization. Creating a solid logical network scheme will allow for scalability, segmentation and routing efficiency.
For the second question, if it's a point to point connection you could use a fiber optic for the connection:
you're looking at ethernet 1000 Base LX (max of 1804 ft).
Cordially,
Ronnie Wong
Host, ITProTV