If p squares of each side 1mm makes a square of side 1cm, then p is

Options

A. 10
B. 100
C. 1000
D. 10000

Answer

To solve the problem of finding the value of \( p \) when \( p \) squares of each side 1 mm make a square of side 1 cm, we can follow these steps:

### Step 1: Understand the dimensions
We know that:
- The side of the larger square is 1 cm.
- The side of each smaller square is 1 mm.

### Step 2: Convert units
Since we want to compare the areas, we need to convert the side of the larger square from centimeters to millimeters.
- 1 cm = 10 mm.

### Step 3: Calculate the area of the larger square
The area \( A \) of the larger square can be calculated using the formula for the area of a square, which is:
\[ A = \text{side} \times \text{side} \]
So,
\[ A = 10 \text{ mm} \times 10 \text{ mm} = 100 \text{ mm}^2 \]

### Step 4: Calculate the area of one smaller square
The area \( a \) of one smaller square (with side 1 mm) is:
\[ a = 1 \text{ mm} \times 1 \text{ mm} = 1 \text{ mm}^2 \]

### Step 5: Relate the areas
Since \( p \) smaller squares make up the area of the larger square, we can express this relationship as:
\[ \text{Area of larger square} = p \times \text{Area of one smaller square} \]
This gives us the equation:
\[ 100 \text{ mm}^2 = p \times 1 \text{ mm}^2 \]

### Step 6: Solve for \( p \)
To find \( p \), we can rearrange the equation:
\[ p = \frac{100 \text{ mm}^2}{1 \text{ mm}^2} = 100 \]

### Conclusion
Thus, the value of \( p \) is \( 100 \).