A router knows three possible routes to reach the same destination network: an OSPF route with metric 782, a RIPv2 route with metric 4, and an EIGRP route with composite metric 20514560. Which route will the router install in the routing table and use for forwarding?

Introduction / Context:
Routing protocols such as RIPv2, OSPF, and EIGRP each use their own internal metric to select the best path within that protocol. However, when a router learns the same destination network from multiple routing protocols at the same time, it cannot compare the metrics directly because they represent different scales and meanings. Instead, Cisco routers use administrative distance to select the preferred protocol first. This question emphasizes how the router chooses the final active route when OSPF, RIPv2, and EIGRP all know a path to the same network.

Given Data / Assumptions:

• One OSPF route exists with metric 782.
• One RIPv2 route exists with metric 4.
• One EIGRP route exists with composite metric 20514560.
• All three describe the same destination network prefix.
• Default administrative distances have not been changed.

Concept / Approach:
Cisco routers do not compare metrics between routing protocols. Instead, they assign an administrative distance to each protocol to indicate the trust level of that source. The lower the administrative distance, the more preferred the route. Default values are: EIGRP internal routes 90, OSPF 110, and RIPv2 120. Therefore, even though RIPv2 may show a small hop count metric and OSPF has a relatively small cost, the router first compares administrative distance and chooses the protocol with the lowest value, which in this case is EIGRP.

Step-by-Step Solution:
1. List default administrative distances: - EIGRP internal: 90. - OSPF: 110. - RIPv2: 120. 2. Ignore the numeric values of the metrics (782, 4, and 20514560) for comparison between protocols because they are not directly comparable. 3. Compare the administrative distance values instead. The smallest value represents the preferred source of the route. 4. EIGRP has distance 90, which is lower than 110 and 120. 5. Therefore, the router installs the EIGRP route in the routing table and uses it for forwarding traffic to the destination network.

Verification / Alternative check:
In a lab, you can configure all three protocols on a router and advertise the same network from different neighbours. Using show ip route, you will see the final chosen route with code D for EIGRP if default distances are used. If you then manually modify administrative distances, for example by increasing EIGRP distance above 110 or lowering OSPF distance below 90, you can observe how the selected route changes in the routing table. This practical experiment confirms that administrative distance, not metric value across protocols, drives the final decision.

Why Other Options Are Wrong:
RIPv2 route because it has the lowest hop count: Hop count is only meaningful within RIP itself. Across protocols, hop count is not compared to EIGRP or OSPF metrics.
OSPF route because its metric is numerically smallest: OSPF metric 782 cannot be compared to RIPv2 hop count or EIGRP composite metrics. The router ignores this comparison across protocols.
All three routes are installed as equal cost paths: Equal cost load balancing is only done within a single protocol when metrics are equal. Here, protocols differ and administrative distance chooses one protocol only.
None, the router cannot choose between different protocol metrics: The router uses administrative distance explicitly for this purpose, so it can choose without difficulty.

Common Pitfalls:
A frequent misunderstanding is to assume that the numerically smallest metric among all protocols will always win, regardless of which protocol generated it. This is not correct. Another pitfall is failing to remember the default distances and therefore incorrectly predicting which protocol will dominate. To avoid such issues, always keep a small reference of default administrative distances in mind, and remember that this parameter is the key to understanding the routing table when multiple protocols coexist.

Final Answer:
EIGRP route because it has the lowest administrative distance