Final answer:
When a blueprint indicates "1/2" = 1', it represents the scale used. This means every half inch on the blueprint corresponds to one foot in real life. Scale drawings require the use of ratios to determine the accurate representation of real-life dimensions.
Step-by-step explanation:
On a blueprint, a note that says "1/2" = 1' indicates the scale at which the drawing is made compared to the actual size of the object being represented. In this scenario, it means that for every half inch (1/2 inch) on the blueprint, it corresponds to one foot (1 foot) in real life. Understanding scales is crucial for creating accurate representations of objects in a smaller, manageable size.
When applying this scale to calculate dimensions for a scale model or drawing, we use ratios to compare the blueprint measurements or 'scale distances' to the actual distances. For example, if Rano has a rectangular backyard that is 50 feet by 30 feet, and he wants to make a scale drawing using a scale of 1/2 inch = 5 feet, he would set up the ratio 0.5 inches/5 feet and use it to find the dimensions for his scale drawing.
Example 4.8.1.2
Rano wants to make a scale drawing of his 50 feet by 30 feet backyard using a scale of 1/2 inch = 5 feet. The dimensions for Rano's backyard in the scale drawing would be calculated as follows:
- For the length (50 feet), the scale drawing would be 50 feet / 5 feet per 1/2 inch = 10 halves of an inch, which is 5 inches.
- For the width (30 feet), the scale drawing would be 30 feet / 5 feet per 1/2 inch = 6 halves of an inch, which is 3 inches.
Therefore, the scale drawing of Rano's backyard would measure 5 inches by 3 inches.
If a student had a blueprint where the scale was 1 inch = 10 feet, and the drawing measured 10 inches by 14 inches, the actual dimensions of the building would be 100 feet by 140 feet.
Understanding the concept of scaling is vital in various fields, such as architecture, engineering, and geography. It allows professionals to represent large objects on a smaller scale, which is easier to handle and understand.