Saphyr and her friends are going to their local concert hall to see their favourite singer, Tinker Leisurely.
The rectangular hall is to be set up so that people sit in rows of chairs facing the stage. Each row will have the same number of seats, with each row having at most \(50\) seats. The hall has a capacity for at most \(115\) rows. Saphyr has discovered that there are to be \(4032\) seats for the audience.
Using what you know about the area of a rectangle and about the whole numbers that divide evenly into \(4032\), determine the possible configurations of seats in the hall.
If the stage is \(36\,\)m wide and the chairs are to be spaced \(1\,\)m apart (from centre to centre), which of your answers in part (a) do you think gives the most reasonable dimensions for the seating? Why?
Theme: Number Sense