On a map `(1)/(2)` cm shows 150 km on the ground. If two cities are 450 km apart on the ground, then the distance between them on the map is

Options

A. 6 cm
B. 1.5 cm
C. 2 cm
D. 2.5 cm

Answer

To solve the problem step by step, we will use the information given about the map's scale and apply the unitary method.

### Step 1: Understand the scale of the map
The problem states that \( \frac{1}{2} \) cm on the map represents 150 km on the ground.

### Step 2: Find the distance represented by 1 km on the map
To find out how many centimeters represent 1 km on the map, we can set up a proportion based on the scale given:

\[ \frac{1}{2} \text{ cm} \text{ represents } 150 \text{ km} \]

To find the distance for 1 km, we can divide both sides by 150:

\[ \text{Distance for 1 km} = \frac{\frac{1}{2} \text{ cm}}{150} = \frac{1}{2 \times 150} = \frac{1}{300} \text{ cm} \]

### Step 3: Calculate the distance for 450 km
Now that we know that 1 km is represented by \( \frac{1}{300} \) cm, we can find the distance on the map for 450 km:

\[ \text{Distance for 450 km} = 450 \times \frac{1}{300} \text{ cm} \]

### Step 4: Simplify the calculation
Calculating this gives:

\[ \text{Distance for 450 km} = \frac{450}{300} \text{ cm} = \frac{3}{2} \text{ cm} \]

### Step 5: Convert to decimal form
To express \( \frac{3}{2} \) cm in decimal form:

\[ \frac{3}{2} = 1.5 \text{ cm} \]

### Final Answer
Thus, the distance between the two cities on the map is **1.5 cm**.

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