How many bricks whose length and breadth are 12 cm and 6 cm, respectively, will be needed to fit in a rectangular region that measures `90 cm xx 120 cm` ? 

Options

A. 200
B. 150
C. 250
D. 100

Answer

To find out how many bricks are needed to fit in a rectangular region measuring 90 cm by 120 cm, we will follow these steps:

### Step 1: Calculate the area of one brick.
The dimensions of one brick are given as:
- Length = 12 cm
- Breadth = 6 cm

The area \( A \) of one brick can be calculated using the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values:
\[ A = 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2 \]

### Step 2: Calculate the area of the rectangular region.
The dimensions of the rectangular region are given as:
- Length = 90 cm
- Breadth = 120 cm

The area \( A_r \) of the rectangular region can be calculated using the same formula:
\[ A_r = \text{Length} \times \text{Breadth} \]
Substituting the values:
\[ A_r = 90 \, \text{cm} \times 120 \, \text{cm} = 10800 \, \text{cm}^2 \]

### Step 3: Determine the number of bricks needed.
Let \( n \) be the number of bricks needed. The total area covered by \( n \) bricks is equal to the area of the rectangular region. Therefore, we can set up the equation:
\[ n \times \text{Area of one brick} = \text{Area of rectangular region} \]
Substituting the areas we calculated:
\[ n \times 72 \, \text{cm}^2 = 10800 \, \text{cm}^2 \]

### Step 4: Solve for \( n \).
To find \( n \), we can rearrange the equation:
\[ n = \frac{10800 \, \text{cm}^2}{72 \, \text{cm}^2} \]
Calculating this gives:
\[ n = 150 \]

### Conclusion:
Therefore, the number of bricks needed to fit in the rectangular region is \( \boxed{150} \).

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