Scale drawings: word problems

Learning Objectives Interpret and write scales in different formats (e.g., ratio, verbal). Set up and solve proportions to find unknown actual lengths from a scale drawing. Set up and solve proportions to find unknown drawing lengths from actual object dimensions. Calculate a unitless scale factor by converting units. Solve word problems involving the perimeter of objects represented in scale drawings. Solve word problems involving the area of objects represented in scale drawings by applying the square of the scale factor. Determine the appropriate scale for a drawing given specific constraints. Ever wondered how architects fit an entire skyscraper on a single sheet of paper or how Google Maps shows your entire city on your phone screen? 🗺️ Let's find out! This tuto...

TermDefinitionExample Scale DrawingA proportional two-dimensional drawing of an object. It is either a reduction or an enlargement of the actual object.A blueprint of a house is a scale drawing where 1 cm on the paper might represent 2 meters of the actual house. ScaleThe ratio that compares the measurement of the drawing to the corresponding measurement of the actual object. It can be written with units.1 cm : 5 m or 1 inch = 10 feet. This means every 1 cm on the drawing corresponds to 5 meters in reality. Scale Factor (k)A unitless ratio that describes how much larger or smaller the drawing is compared to the actual object. To find it, the units must be the same.If the scale is 1 cm : 5 m, we convert 5 m to 500 cm. The scale factor is k = 1/500. ProportionAn equation stating that two ra...

The Proportion Formula \frac{\text{drawing length}}{\text{actual length}} = \frac{\text{drawing length}}{\text{actual length}} This is the fundamental setup for solving most scale drawing problems. You use the given scale as one ratio and the given measurement with its unknown counterpart as the other ratio. Scale Factor Formula k = \frac{\text{drawing dimension}}{\text{actual dimension}} \quad (\text{in same units}) Use this to find the unitless scale factor, 'k'. You must convert both dimensions to the same unit (e.g., both to cm) before dividing. If k < 1, it's a reduction. If k > 1, it's an enlargement. Area Scaling Formula \text{Actual Area} = (\text{Drawing Area}) \times k^{-2} \quad \text{or} \quad \text{Actual Area} = (\text{Drawing Ar...