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 option is 5.

To arrange 48 small squares of size 1 cm × 1 cm into a rectangle, the total area formed will always be 48 cm² because:

Area = Number of squares × Area of each square

$\text{Area}=48\times (1\text{ cm}\times 1\text{ cm})=48{\text{ cm}}^2$

The number of ways to arrange these 48 squares into different rectangular shapes corresponds to the number of distinct factor pairs of 48 (where length and width are integer dimensions in cm).

Let the dimensions of the rectangle formed be $a$ cm and $b$ cm, such that:

$a\times b=48$

Now, let's find all unique factor pairs of 48:

1. $1\times 48=48$ (1 row of 48 squares)

2. $2\times 24=48$ (2 rows of 24 squares)

3. $3\times 16=48$ (3 rows of 16 squares)

4. $4\times 12=48$ (4 rows of 12 squares)

5. $6\times 8=48$ (6 rows of 8 squares)

Therefore, there are 5 different ways to arrange 48 small squares to form a resulting area of 48 cm².