Construct a diagonal scale of representative fraction = (1/36) showing yard, foot and inch. Scale should be long enough to measure 5 yard. Measure 3 yard, 2 foot, and 9 inch.
Understand the Problem
The question is asking to construct a diagonal scale with a specific representative fraction and dimensions that allow measuring up to 5 yards. It also requires measuring a distance specified in yards, feet, and inches. The approach to solve this would involve calculating the scale's dimensions, drawing the scale accordingly, and marking the required measurements on it.
Answer
The scale can measure distances up to $5$ yards or $180$ inches.
Answer for screen readers
The construction process results in a diagonal scale that can accurately measure distances up to 180 inches (15 feet or 5 yards), incorporating the specified units of measurement.
Steps to Solve
- Determine the Representative Fraction (RF)
Begin by understanding that the representative fraction is the ratio of a distance on the scale to the actual distance. For example, if your RF is 1:100, it means 1 unit on the scale represents 100 units in real life.
- Calculate the Dimensions of the Scale
For a scale that can measure up to 5 yards (which is equal to 15 feet), determine the length of the scale.
Convert 5 yards to inches: $$ 5 \text{ yards} \times 36 \text{ inches/yard} = 180 \text{ inches} $$
- Determine the Length of Each Unit on the Scale
Divide the length of the scale by the number it is meant to measure, based on the RF. For instance, if measuring in yards, and your RF is 1:10: $$ \text{Length of scale} = \frac{180 \text{ inches}}{10} = 18 \text{ inches} $$
- Draw the Scale
Using a ruler, draw a straight line that matches the calculated length (for example, 18 inches). Divide this line into segments that reflect the measurements you want to mark.
- Mark Measurements in Yards, Feet, and Inches
Label the segments appropriately, ensuring to show clear markings for yards, feet, and inches along the line you drew.
For example, each segment of 6 inches represents 1 foot, and you can mark every 12 inches as 1 yard.
- Final Touches
Make sure to verify that the distances labeled are consistent with your RF and that they accurately represent the lengths they stand for.
The construction process results in a diagonal scale that can accurately measure distances up to 180 inches (15 feet or 5 yards), incorporating the specified units of measurement.
More Information
A diagonal scale is particularly useful for measuring various dimensions in a single line, making it versatile for different real-world applications. Such scales are widely utilized in engineering and drawing.
Tips
- Miscalculating the RF or length conversion which can lead to incorrect scale dimensions.
- Not dividing the scale line correctly into segments can cause confusion in reading measurements.
- Forgetting to label segments can lead to ambiguity in interpretation.
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