OPENING PROBLEM A square garden gazebo is surrounded by 4 semi-circles of
lawn as shown.
For a wedding, quarter circles of flowers are planted in
each corner of the gazebo. The lawn covers 4 times as
much area as the flower beds.
Suppose the flower beds are metres apart as shown.
2 m
Things to think about:
10 m
a Explain why the radius of each flower bed is 5
b Hence, show that 22 – 20x + 50 = 0.
c By solving this equation, can you find the distance between the flower beds?