Ada Lovelace Public School needs to add a new wing to its main
building that includes a classroom, library, staff room, and washroom.
The plans for the addition are shown, with all new rooms being
rectangular; however, some of the measurements are missing.
A floor plan with the four rooms, each represented by a rectangle with two horizontal
sides (top and bottom) and two vertical sides (left and right).
The library is in the top left corner. Its vertical sides are 8
metres long and its horizontal sides are 10 metres long.
The staff room is to the right of the library. The left side of the
staff room lines up exactly with the right side library. The horizontal
sides of the staff room are shorter than the vertical sides, but there
are no measurements given.
The classroom is below the library. The top side of the classroom
lies along the bottom side of the library and the left sides of the two
rooms line up. The horizontal sides of the classroom are just over half
the length of the horizontal sides of the library. The vertical sides of
the classroom are longer than the horizontal sides, but there are no
measurements given.
The washroom is below the classroom. The top side of the washroom
lines up exactly with the bottom side of the classroom. The vertical
sides of the washroom are 3 metres long and the horizontal sides are 6
metres long.
Fortunately, the contractor remembered the following extra
details:
The length of the classroom is three times the width of the
washroom.
The width of the staff room is half the length of the
library.
When describing the dimensions of a rectangle, the contractor uses
length to describe the longer side, and width to
describe the shorter side.
What are the missing dimensions of the classroom and the staff
room?
What is the total floor area of the four new rooms?
