Ammini is arranging 36 identical squares in the form of different rectangles. How many different types of rectangles can she make with these squares ?

The correct option is Five.

To find how many different types of rectangles Ammini can make using 36 identical unit squares, we need to determine the number of different pairs of dimensions (length and width) that multiply together to give a total area of 36 square units.

Mathematically, we look for all factor pairs of 36.

Let the length and width of the rectangle be whole numbers $a$ and $b$.

The area of the rectangle is given by:

$a\times b=36$

Now, let us list all pairs of positive integers whose product is 36:

1. $1\times 36=36$ (1 row of 36 squares)
2. $2\times 18=36$ (2 rows of 18 squares)
3. $3\times 12=36$ (3 rows of 12 squares)
4. $4\times 9=36$ (4 rows of 9 squares)
5. $6\times 6=36$ (6 rows of 6 squares, which forms a square, a special type of rectangle)

Note that pairs like $9\times 4$ or $12\times 3$ represent the same physical rectangles rotated, so they do not count as distinct types.

Therefore, there are 5 different types of rectangles that can be formed using 36 identical squares.