Scale Drawings & Models

Scale Drawings & Models Distances on a scale drawing or model are proportional to real-life distances. The scale is determined by the ratio of a length on a drawing or model to its corresponding actual length.

Examples The local school district has made a scale model of a campus of Engels Middle School including a proposed new building. The scale of the model is 1 inch = 3 feet. New Building Gym Parking Academic Building

Example Continued… An existing gym is 8 inches tall in the model. How tall is the actual gymnasium? Set up a proportion… 1 8 3 X New Building Gym = Parking Academic Building 1(x) = 3(8) X = 24 feet tall

To find the scale factor for scale drawings and models, write the ratio given by the scale in simplest form. Write the ratio of 1 inch to 1 feet in simplest form. 1 inch 1 in. 1 Feet 16 in. 1 3 Conversion: 1 foot = 12 inches = 1 3

= Example… 0.5 inch 5 inch 3 miles X miles 4 On a map, two cities are 5 inches apart. The scale of the map is 0.5 inch = 3 miles. What is the actual distance between the towns? Set up a proportion. 3 4 0.5X = 3(5 ) 0.5X = 17.25 X = 34.5 miles 3 4 0.5 inch 5 inch 3 miles X miles =

Example Set up a proportion. = Marta is making a scale drawing of her apartment for a school project. The apartment is 28 feet wide. On her drawing, the apartment is 7 inches wide. What is the scale of Marta’s drawing? Set up a proportion. 28 feet 28 feet 4 feet 7 inches 1 inch = 1 inch = 4 feet