In a rectangular room, detectors must be placed with a certain spacing: how many are needed if the layout requires 15 feet from walls and 30-foot spacing?

In a rectangular room, detectors must be placed with a certain spacing: how many are needed if the layout requires 15 feet from walls and 30-foot spacing?

• A. 3
• B. 4
• C. 5
• D. 6

Answer: (C)

Think about placing detectors on a grid while keeping a 15-foot offset from every wall and no more than 30 feet between neighboring detectors. If you look at a typical rectangular room, subtract 15 feet from each wall, leaving a central usable area that’s 30 by 30 feet. Put detectors at the four corners of that central square (each is 15 feet from the adjacent walls). They’re 30 feet apart along the walls, and each sits safely at the required distance from a wall. To ensure the room’s center isn’t too far from a detector, add one more right in the middle of the room. In a 60 by 60-foot room, the center is about 21 feet from any corner detector, so the 30-foot spacing rule is respected, and no area is left uncovered. This arrangement uses five detectors, which matches the given answer.

Think about placing detectors on a grid while keeping a 15-foot offset from every wall and no more than 30 feet between neighboring detectors. If you look at a typical rectangular room, subtract 15 feet from each wall, leaving a central usable area that’s 30 by 30 feet. Put detectors at the four corners of that central square (each is 15 feet from the adjacent walls). They’re 30 feet apart along the walls, and each sits safely at the required distance from a wall. To ensure the room’s center isn’t too far from a detector, add one more right in the middle of the room. In a 60 by 60-foot room, the center is about 21 feet from any corner detector, so the 30-foot spacing rule is respected, and no area is left uncovered. This arrangement uses five detectors, which matches the given answer.