24 CEMO UWATERLOOCA I The CENTRE for EDUCATION IN MATHEMATICS and COMPUTING
Problem of the Week
Problem C
Making a Splash!
A fanily has decided that they want to have a pool installed in their backyard. The city they
live in has a by-law which states, "No pool may occupy more than 20% of the total area of the
backyard in which it is to be installed."
Their backyard is rectangular and measures 24 m by 18 m. The family creates a design in
which they divide their backyard into a 3 by 3 grid of sune identical rectangles. The pool will
be circular with the circumference of the pool passing through the four vertices of the middle
rectangle. The middle rectangle will be completely covered by the pool. The distance across
the pool through its centre will equal the length of the diagonal of the middle rectangle. Their
plan is illustrated on the diagram below.
Should their plan be approved by the city?
18 m
24 m