Lesson 2: Scale Drawings

Property

A scale drawing is a proportional two-dimensional (2D) drawing of an object. The scale is the ratio that relates the dimensions in the drawing to the actual dimensions of the object.
Scale = Drawing Dimension : Actual Dimension

Examples

• On a road map, the scale might be 1 inch : 10 miles. This means every 1 inch on the map represents an actual distance of 10 miles.
• The blueprint for a house uses a scale of 1/4 inch = 1 foot. Every quarter-inch on the drawing corresponds to 1 foot of the actual house.
• A drawing of an insect in a science textbook might have a scale of 5 cm : 1 cm. This indicates the drawing is 5 times larger than the actual insect.

Explanation

Scale drawings are used to accurately represent objects that are either too large or too small to be drawn at their actual size on paper. The scale ensures that all parts of the drawing are shrunk or enlarged by the same factor, maintaining the object's correct proportions.

Property

Scale notations express the relationship between drawing measurements and actual measurements in three common formats: ratio form ($1:100$), unit form ($1 \text{ inch} = 5 \text{ feet}$), and fraction form ($\frac{1}{100}$).

Examples

Property

To find missing measurements, set up a simple fraction proportion: $\frac{\text{Drawing}}{\text{Actual}} = \frac{\text{Drawing}}{\text{Actual}}$.
Crucial Rule: If your scale does not specify units (like 1:50), you MUST make sure both your drawing and actual measurements are converted to the exact same unit before doing the math.

Examples

• Finding Actual Distance (Unit Form): A map scale is 1 cm = 10 km. Two cities are 4.5 cm apart on the map.
  • Math: 4.5 * 10 = 45. The cities are 45 km apart.
• Finding Actual Distance (Ratio Form): A model boat has a scale of 1:30. The model is 15 cm long. How long is the real boat in meters?
  • Step 1: 15 cm * 30 = 450 cm (Real boat length in cm).
  • Step 2: Convert to meters. 450 cm = 4.5 m.
• Finding Drawing Length: A room is actually 14 feet wide. The blueprint scale is 1 inch = 4 feet.
  • Math: 14 / 4 = 3.5. Draw it 3.5 inches wide on the paper.

Explanation

When solving these, always keep your labels on your numbers! If you write $\frac{1 \text{ in}}{4 \text{ ft}} = \frac{x \text{ in}}{14 \text{ ft}}$, you can clearly see that you need to cross-multiply or divide. If a problem gives you a unitless ratio like 1:300 but asks for the real answer in meters, always calculate the real answer in the tiny unit (like centimeters) first, and do the conversion at the very end.