Question 5
A rectangular carpet is placed in an $$8\text{ m} \times 8\text{ m}$$ room as shown. What fraction of the floor is not covered?
[image]
Solution
From the grid, the carpet has perpendicular side lengths $$6\sqrt2$$ and $$2\sqrt2$$. Its area is therefore $$6\sqrt2 \times 2\sqrt2=24$$, while the room area is $$8 \times 8=64$$. The uncovered fraction is $$\frac{64-24}{64}=\frac{5}{8}$$.
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