This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to construct the plain scale: A plain scale is used to represent two consecutive units (e.g., yards and feet, or meters and decimeters). Step 1: Calculate the Representative Fraction (RF). The scale is given as 1 foot (actual length) = 1.5 inches (drawing length). We need to express both in the same units to find the RF. We know that 1 foot = 12 inches. RF = Drawing lengthActual length = 1.5 inches1 foot = 1.5 inches12 inches = (1.5)/(12) = (15)/(120) = (1)/(8) The Representative Fraction is (1)/(8). Step 2: Determine the Length of the Scale (LOS). The scale needs to be long enough to measure up to 4 feet and read yards and feet. Since 1 yard = 3 feet, 4 feet is 1 yard and 1 foot. To have clear yard divisions, it's practical to make the total length of the scale represent a whole number of yards that covers 4 feet. The smallest such whole number is 2 yards (which is 6 feet). LOS = RF × Maximum actual length to be represented LOS = (1)/(8) × 2 yards Convert 2 yards to inches: 2 yards = 2 × 3 feet = 6 feet = 6 × 12 inches = 72 inches. LOS = (1)/(8) × 72 inches = 9 inches The total length of the scale to be drawn is 9 inches. Step 3: Construct the Scale. Draw a straight line 9 inches long. Draw another line parallel to it, about 0.5 inches above, to form a narrow rectangle. Close the ends. Step 4: Divide into Primary Divisions (Yards). The 9-inch line represents 2 yards. Divide this line into 2 equal parts. Each part will be 4.5 inches long and represent 1 yard. Mark the point at 4.5 inches from the left as '0'. Mark the point at 9 inches (the right end) as '1 YARD'. (The question asks to read yards, so we can label the rightmost mark as 1 YARD, and the 0 mark as the start of the yards section). Label the rightmost division 'YARDS'. Step 5: Divide the Leftmost Primary Division into Secondary Divisions (Feet). The segment from '0' to the left end (4.5 inches long) represents 1 yard. Since 1 yard = 3 feet, divide this 4.5-inch segment into 3 equal parts. Each part will be 1.5 inches long and represent 1 foot. Mark these divisions to the left of '0' as '1', '2', and '3'. The '3' mark will be at the extreme left end. Label this section 'FEET'. Step 6: Final Touches. Add the title "PLAIN SCALE" and state the RF = 1:8. The scale is now constructed to read yards and feet, and can measure up to 4 feet (e.g., by taking 1 YARD from the right section and 1 FOOT from the left section, which totals 3 feet + 1 foot = 4 feet). Here is a conceptual diagram of the constructed scale: ` <-----------------------------------------------------------------------------------------------------> | 1 ft | 1 ft | 1 ft | 1 yard | | | | | | <-----------------------------------------------------------------------------------------------------> 3 2 1 0 1 YARD (FEET) (YARDS) RF = 1:8 ` Drop the next question.