year 8 maths

124 Chapter 3 Measurement and Pythagoras’ theorem
ENRICHMENT
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15
Disappearing squares
15 A square is drawn with a particular side length. A second square is drawn inside the square so that its
side length is one-third that of the original square. Then a third square is drawn, with side length of
one-third that of the second square and so on.
a
What is the minimum number of squares that would need to be drawn in this pattern (including the
starting square) if the innermost square has a perimeter of less than one-hundredth the perimeter of
the outermost square?
b Now imagine the situation is reversed and each square’s perimeter is three times larger than the
next smallest square. What is the minimum number of squares that would be drawn in total if
the perimeter of the outermost square is to be at least 1000 times the perimeter of the innermost
square?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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