mathschallenge.net

Problem

A company that specialises in fitting false ceilings uses a design based on 1m² ceiling tiles arranged in a grid.

Each tile is supported by metal strips that slot together.

Find the total length of metal strips required to fit this design in a room measuring 3 m by 4 m.

Solution

Consider the 4x3 grid.

The grid consists of 5 vertical strips of 3 units and 4 horizontal strips of 4 units.
So total length of metal strips = 5 3 + 4 4 = 15 + 16 = 31 m.

What if the room measured m x n?
What if m or n are not integers?