The dimensions of the model of a multistorey building are `1.2 m xx 75 cm xx 2 m`. If the scale factor is 1 : 30, find the actual dimensions of the building. 

Answer

To find the actual dimensions of the building from the model dimensions given a scale factor, we can follow these steps:

### Step 1: Convert all dimensions to the same unit
The dimensions of the model are given as:
- Length = 1.2 m
- Breadth = 75 cm
- Height = 2 m

First, we need to convert the breadth from centimeters to meters. We know that:
1 meter = 100 centimeters

So, we can convert 75 cm to meters:
\[ 75 \text{ cm} = \frac{75}{100} \text{ m} = 0.75 \text{ m} \]

Now, the dimensions of the model in meters are:
- Length = 1.2 m
- Breadth = 0.75 m
- Height = 2 m

### Step 2: Use the scale factor to find actual dimensions
The scale factor is given as 1:30, which means:
\[ \text{Scale Factor} = \frac{\text{Length of model}}{\text{Length of building}} = \frac{1}{30} \]

From this, we can express the actual dimensions of the building as:
\[ \text{Length of building} = \text{Length of model} \times 30 \]
\[ \text{Breadth of building} = \text{Breadth of model} \times 30 \]
\[ \text{Height of building} = \text{Height of model} \times 30 \]

### Step 3: Calculate the actual dimensions
1. **Length of the building**:
\[ \text{Length of building} = 1.2 \text{ m} \times 30 = 36 \text{ m} \]

2. **Breadth of the building**:
\[ \text{Breadth of building} = 0.75 \text{ m} \times 30 = 22.5 \text{ m} \]

3. **Height of the building**:
\[ \text{Height of building} = 2 \text{ m} \times 30 = 60 \text{ m} \]

### Final Result
The actual dimensions of the building are:
- Length = 36 m
- Breadth = 22.5 m
- Height = 60 m

Thus, the dimensions of the new building are:
\[ 36 \text{ m} \times 22.5 \text{ m} \times 60 \text{ m} \]

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