Final answer:
To find the actual length Wally needs for his diagonal cut, ratios and proportions based on scale factors must be used. Calculations are made to convert measurements from scale to actual sizes, ensuring accuracy for various applications including design and mapping.
Step-by-step explanation:
To determine the length of the cut Wally needs to make, we need to understand the concept of scale drawings and use proportions to find the actual length. The process involves setting up ratios and proportions to convert scale measurements into actual distances based on the given scale factor.
For example, if we have a scale that states 1 inch equals 2000 miles, and we need to find out the actual distance for a scale measurement of 0.5 inches, we can set up the following proportion: 1 inch/2000 miles = 0.5 inches/x miles. Solving for x would give us the actual distance. Similarly, using a scale measurement of 3 inches, the proportion is: 1 inch/2000 miles = 3 inches/x miles.
When measuring objects directly with a ruler, we might encounter situations where the measurement falls between tick marks. As an example, measuring an object as 1.36 cm means we are using estimation to determine that the object is six-tenths of the way between the third and fourth tick mark.
In applications such as architectural modeling, we may deal with converting scale lengths to actual sizes using proportions like Length=1/20=0.5/5 or Width=w/10=0.5/5, representing different scale factors for length and width. Understanding these conversions is critical in disciplines like engineering, architecture, and cartography.