Certainly! Let's analyze the situation step by step to see how many squares can be found in a 2 by 3 rectangle.
### Step-by-Step Analysis
1. Count the individual 1x1 squares:
- The rectangle is divided into a grid of 2 rows and 3 columns.
- Each cell in this grid represents a 1x1 square.
- There are [tex]\( 2 \times 3 = 6 \)[/tex] such 1x1 squares.
2. Count the 2x2 squares:
- For a square of size 2x2, you need a 2x2 section of the grid.
- These 2x2 squares can only fit in the top left, and the top right section of the rectangle since it needs at least 2 rows and 2 columns together.
- You can place one 2x2 square in each possible 2x2 section.
- Here, you can have [tex]\( 1 \times 2 = 2 \)[/tex] such 2x2 squares.
3. Count the 1x2 rectangles as squares:
- When considering a complete 2x3 rectangle, the options for differing dimensions can be extensive, but as squares must be an equal dimension sides.
- 1x2 size structure is rectangular, hence cannot opt for square enumeration separately in these terms.
4. Count bigger squares, like 3x3, 1x3, 2x3, or 3x2 options:
- Not applicable, as the 2x3 rectangle dimensions (2 length and 3 width cannot accommodate beyond in square forms more completely honoring being 'a square' needs)
When we sum up all the counted squares:
- [tex]\(6\)[/tex] (1x1 squares)
- [tex]\(2\)[/tex] (2x2 squares)
Thus the total number of squares in a 2 by 3 rectangle is:
[tex]\[ 6 + 2 = 8 \][/tex]
Therefore, the answer to the question of how many squares a 2 by 3 rectangle contains is 8.
