The scale of map is 1 : 50,000. In the map, a triangular plot ABC of land has the following dimensions :
`AB = 2 cm, BC = 3.5 cm ` and angle `ABC = 90^@`.
Calculate : the actual length of side BC, in km, of the land.

Answer

To solve the problem, we need to calculate the actual length of side BC of the triangular plot ABC based on the given map scale. Here’s the step-by-step solution:

### Step 1: Understand the Scale of the Map
The scale of the map is given as 1 : 50,000. This means that 1 unit on the map corresponds to 50,000 units in reality.

### Step 2: Identify the Length of Side BC on the Map
The length of side BC on the map is given as 3.5 cm.

### Step 3: Calculate the Actual Length of Side BC
To find the actual length of side BC, we need to multiply the length on the map by the scale factor:
\[ \text{Actual Length of BC} = \text{Length on Map} \times \text{Scale Factor} \]
\[ \text{Actual Length of BC} = 3.5 \, \text{cm} \times 50,000 \]

### Step 4: Perform the Multiplication
Calculating the multiplication:
\[ 3.5 \times 50,000 = 175,000 \, \text{cm} \]

### Step 5: Convert Centimeters to Kilometers
To convert centimeters to kilometers, we use the conversion factor:
\[ 1 \, \text{km} = 100,000 \, \text{cm} \]
Thus, to convert 175,000 cm to kilometers:
\[ \text{Length in km} = \frac{175,000 \, \text{cm}}{100,000} \]
\[ \text{Length in km} = 1.75 \, \text{km} \]

### Final Answer
The actual length of side BC is **1.75 km**.

---