Final answer:
To find the length of side x, we create proportions based on the provided scale ratios and solve for x using cross-multiplication. This concept uses a scale factor to convert scale measurements to actual measurements while ensuring unit consistency.
Step-by-step explanation:
To find the length of side x to the nearest tenth, we use the concept of ratios that compare scale measurements to actual measurements. When working with scale models or drawings, a scale factor is used to convert from one measurement to another.
Let's investigate several scenarios:
- For the first ratio, we are given a scale length of 8 inches and need to find the actual length represented by x. The ratio provided is 0.5 inch/20 miles = 8 inches/x miles. To solve this, we set up a proportion: (0.5/20) = (8/x) and solve for x by cross-multiplication.
- If we have a scale factor of 1 inch to 2000 miles with a scale length of 0.25 inches, the ratio to find x would be 1 inch/2000 miles = 0.25 inches/x miles. Applying the same method of cross-multiplication, we can solve for x.
- In another instance, if the scale length is 3 inches and we want to find the actual length x, using the ratio 0.5 inches/75 miles = 3 inches/x miles, we apply cross-multiplication again to solve for x.
To maintain unit consistency, we also use ratios for inches to feet conversion, such as 1/20 for length and w/10 for width when dealing with buildings or maps.
Regarding measurements with rulers, the uncertainty of the tenths digit in a measurement between 2 and 3 cm is noted. It's important to report the tenths digit with as much accuracy as the ruler allows