Scale drawings word problems

Learning Objectives Interpret a scale on a map or blueprint and write it as a ratio. Calculate a unitless scale factor by converting units to be identical. Set up and solve proportions to find unknown actual dimensions from a scale drawing. Set up and solve proportions to find unknown drawing dimensions for a real-world object. Determine the scale of a drawing when given both the drawing and actual dimensions. Apply scale factor concepts to calculate the actual area of a shape from its scale drawing dimensions. Ever wondered how architects fit an entire skyscraper onto a single piece of paper, or how Google Maps shows a 10-mile route on your phone screen? 🗺️ This tutorial will teach you how to use ratios and proportions to solve scale drawing word problems. You'll lear...

TermDefinitionExample Scale DrawingA proportional two-dimensional drawing of an object that is either a reduction or an enlargement of the actual object.A blueprint of a house is a scale drawing. It is smaller than the actual house but all the proportions are correct. ScaleThe ratio that compares the measurement on a drawing to the corresponding measurement on the actual object.A map scale of `1 cm : 10 km` means that every 1 cm on the map represents 10 km in the real world. Scale FactorA unitless ratio, in simplest form, that shows the relationship between the drawing and actual dimensions. To find the scale factor, the units must be the same.For a scale of `1 inch : 4 feet`, first convert 4 feet to 48 inches. The scale factor is `1/48`. ProportionAn equation stating that two ratios are...

The Proportion Formula \frac{\text{Drawing Dimension 1}}{\text{Actual Dimension 1}} = \frac{\text{Drawing Dimension 2}}{\text{Actual Dimension 2}} Use this formula to find any unknown dimension. Set up the scale as the first ratio and the known measurement with its unknown counterpart as the second ratio. Ensure the units are consistent across the numerators and denominators. Scale Factor Formula k = \frac{\text{Drawing Dimension}}{\text{Actual Dimension}} Use this to find the scale factor (k). Before dividing, you MUST convert both dimensions to the exact same unit (e.g., both in cm, or both in inches). The resulting factor will have no units. Area Relationship \text{Actual Area} = \text{Drawing Area} \times (\frac{1}{k})^2 The ratio of the areas is the square of th...