Practice Scale Drawings in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Creating or interpreting drawings and models where every length is multiplied by the same constant (the scale factor), preserving shape while changing size.
A map is a scale drawing of the real world. If 1 inch on the map equals 10 miles in reality, the scale factor is 1:10\text{ miles}. Every distance on the map uses the same ratio, so the shapes stay accurate—just smaller. Enlarging a photo works the same way in reverse.
Example 1
easyA map has a scale of 1 cm : 50 km. Two cities are 3.5 cm apart on the map. What is the actual distance between the cities?
Example 2
mediumAn architect draws a floor plan with a scale of \frac{1}{4} inch = 1 foot. A room measures 3.5 inches by 2 inches on the drawing. What are the actual dimensions and area of the room?
Example 3
easyA model car is built at a scale of 1:24. The model car is 15 cm long. How long is the actual car in meters?
Example 4
hardA park is drawn on a map using a scale of 2 cm : 300 m. On the map, the park is a rectangle 5 cm by 3 cm. Find the actual area of the park in square meters and in hectares (1 hectare = 10,000 m²).