A map is made with the scale 2 cm = 550km. If the distance between two places in the map is 5.25 cm, find the actual distance between the two places in kilometres and metres.

Answer

To solve the problem step by step, we will follow the given scale and the distance on the map to find the actual distance between the two places in kilometers and meters.

### Step 1: Understand the Scale
The scale of the map is given as:
\[ 2 \text{ cm} = 550 \text{ km} \]

### Step 2: Find the Distance Represented by 1 cm
To find out how many kilometers are represented by 1 cm on the map, we divide the distance by 2:
\[ 1 \text{ cm} = \frac{550 \text{ km}}{2} = 275 \text{ km} \]

### Step 3: Calculate the Actual Distance for 5.25 cm
Now, we need to find the actual distance corresponding to 5.25 cm on the map. We can do this by multiplying the distance in cm by the actual distance represented by 1 cm:
\[ \text{Actual Distance} = 5.25 \text{ cm} \times 275 \text{ km/cm} \]

### Step 4: Perform the Multiplication
Now we will calculate:
\[ 5.25 \times 275 \]
To do this multiplication:
1. \( 5.25 \times 275 = 5.25 \times (200 + 70 + 5) \)
2. Calculate each part:
- \( 5.25 \times 200 = 1050 \)
- \( 5.25 \times 70 = 367.5 \)
- \( 5.25 \times 5 = 26.25 \)

3. Now, add these results together:
\[ 1050 + 367.5 + 26.25 = 1443.75 \text{ km} \]

### Step 5: Convert Kilometers to Meters
To convert kilometers to meters, we multiply by 1000 (since 1 km = 1000 m):
\[ 1443.75 \text{ km} = 1443.75 \times 1000 \text{ m} = 1443750 \text{ m} \]

### Final Answer
The actual distance between the two places is:
- **In kilometers:** 1443.75 km
- **In meters:** 1443750 m