Which equipment should be used for backup, interior attack, and overhaul?

Handlines are essential tools for backup, interior attack, and overhaul in firefighting operations. When engaging in an interior attack, firefighters require a manageable and flexible source of water to help extinguish flames and protect themselves from heat and smoke, and handlines provide that capability.

These hoses allow firefighters to effectively direct water onto the fire from various angles and positions, which is crucial during an interior attack where maneuverability and precision are vital. Additionally, handlines are often used for overhaul operations to ensure any remaining hot spots are properly extinguished to prevent reignition, as they allow firefighters to apply water where needed without the bulk of larger hose lines.

In contrast, other equipment listed, such as rope lines, serve quite different functions, such as providing safety or support for rescue operations. Fire hoses are a more general term that encompasses handlines but doesn't specifically indicate their use in interior attack and overhaul operations. Sprinkler systems are typically part of a building's fire protection system and are not meant for active firefighting by personnel on the scene. Therefore, handlines are the most appropriate equipment for the specified tasks of backup, interior attack, and overhaul, making them the correct answer.