In how many ways, 48 small squares of 1 cm × 1 cm can be arranged so that the resulting area is 48 cm² ?

The correct answer is Option 3 (5).

To find the number of ways to arrange 48 small squares of size 1 cm × 1 cm to form a rectangle with an area of 48 cm², we need to arrange them into a rectangular grid of rows and columns.

Let the dimensions of the rectangle formed by the squares be $a$ cm and $b$ cm, where $a$ and $b$ are positive integers representing the number of squares along the length and width respectively.

The area of the resulting rectangle is given by:

$\text{Area}=a\times b=48$

Therefore, we need to find all pairs of positive integers $(a,b)$ such that their product is equal to 48. Since an arrangement of $a$ × $b$ is visually identical in shape to $b$ × $a$ (just rotated), we consider unordered pairs of factors.

Let us list all pairs of positive integers whose product is 48:

1. $1\times 48=48$

2. $2\times 24=48$

3. $3\times 16=48$

4. $4\times 12=48$

5. $6\times 8=48$

Thus, there are 5 unique rectangular arrangements possible using all 48 small squares.