Scale Drawings Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A map has a scale of 11 cm :50: 50 km. Two cities are 3.53.5 cm apart on the map. What is the actual distance between the cities?

Solution

  1. 1
    Step 1: Identify the scale factor: 11 cm on the map =50= 50 km in reality.
  2. 2
    Step 2: Write the proportion: 1 cm50 km=3.5 cmx km\frac{1 \text{ cm}}{50 \text{ km}} = \frac{3.5 \text{ cm}}{x \text{ km}}.
  3. 3
    Step 3: Solve by cross-multiplying: x=3.5×50=175x = 3.5 \times 50 = 175 km.
  4. 4
    Step 4: The actual distance between the two cities is 175175 km.

Answer

175175 km
Scale drawings use proportional reasoning. The scale ratio 1:50 means every 1 cm on the map represents 50 km in reality. Multiplying the map distance (3.5 cm) by the scale factor (50) gives the actual distance of 175 km.

About Scale Drawings

Creating or interpreting drawings and models where every length is multiplied by the same constant (the scale factor), preserving shape while changing size.

Learn more about Scale Drawings →

More Scale Drawings Examples

Example 2 medium

An architect draws a floor plan with a scale of [formula] inch [formula] foot. A room measures [form

Example 3 easy

A model car is built at a scale of [formula]. The model car is [formula] cm long. How long is the ac

Example 4 hard

A park is drawn on a map using a scale of [formula] cm [formula] m. On the map, the park is a rectan

← All Scale Drawings Examples Scale Drawings Concept