A rectangle is made up of 12 square of side 1 cm. What possible dimensions can the rectangle have ?

Answer

To find the possible dimensions of a rectangle made up of 12 squares of side 1 cm, we can follow these steps:

### Step 1: Understand the total area
The area of the rectangle is equal to the total number of squares. Since each square has an area of 1 cm², the total area of the rectangle is:
\[ \text{Area} = 12 \text{ cm}^2 \]

### Step 2: Find the factors of 12
To determine the possible dimensions of the rectangle, we need to find the pairs of factors of 12. The factors of 12 are:
\[ 1, 2, 3, 4, 6, 12 \]

### Step 3: Pair the factors to form dimensions
Next, we can pair these factors to find the possible dimensions (length and width) of the rectangle. Each pair of factors will represent the dimensions of the rectangle:
- Pair (1, 12): This gives dimensions of \(1 \text{ cm} \times 12 \text{ cm}\)
- Pair (2, 6): This gives dimensions of \(2 \text{ cm} \times 6 \text{ cm}\)
- Pair (3, 4): This gives dimensions of \(3 \text{ cm} \times 4 \text{ cm}\)

### Step 4: List the unique dimensions
We can summarize the unique dimensions of the rectangle as:
1. \(1 \text{ cm} \times 12 \text{ cm}\)
2. \(2 \text{ cm} \times 6 \text{ cm}\)
3. \(3 \text{ cm} \times 4 \text{ cm}\)

### Conclusion
The possible dimensions of the rectangle made up of 12 squares of side 1 cm are:
- \(1 \text{ cm} \times 12 \text{ cm}\)
- \(2 \text{ cm} \times 6 \text{ cm}\)
- \(3 \text{ cm} \times 4 \text{ cm}\)

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