Discussion
In how many ways, 48 small squares of 1 cm × 1 cm can be arranged so that the resulting area is 48 cm2 ?
Answer: C
The squares can be arranged in 5 ways.
Any arrangement of all 48 unit squares covers 48 cm2. Reading the question as asking for rectangles, we need pairs of whole-number sides whose product is 48:
\[ \begin{aligned} 48 &= 1 \times 48 = 2 \times 24 = 3 \times 16 \\ &= 4 \times 12 = 6 \times 8 \end{aligned} \]
That gives five different rectangles; turning one round (8 by 6 instead of 6 by 8) gives the same shape. 48 has exactly these five factor pairs, so 4 and 2 leave some out, and 6 counts one more than exist.
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