A scale drawing of a truck has a length of 3 inches (in.), as shown below. The actual truck has a length of 18 feet (ft). What scale was used for the drawing?
1 inch = 6 feet.
To determine the scale of the drawing, we compare the length of the scale drawing (3 inches) to the actual length of the truck (18 feet). By converting the feet to inches (1 foot = 12 inches), we find that 18 feet equals 216 inches. Thus, for every 1 inch on the scale drawing, there are 6 actual feet (216 inches / 36 inches).
This choice suggests that 6 inches on the drawing corresponds to 1 foot in reality. However, if this were the case, the actual truck length would be represented as 3 inches x 6 = 18 feet, which would imply a different scale ratio and is inconsistent with our calculations.
If this were true, then 3 inches would represent 3 x 15 = 45 feet in reality, which is significantly larger than the actual truck length of 18 feet. Thus, this scale is incorrect as it does not match the given dimensions.
This is the correct choice. Since 3 inches in the scale drawing represents 18 feet in reality (3 inches x 6 feet/inch = 18 feet), this scale accurately reflects the relationship between the drawing and the actual truck's dimensions.
This option implies that 15 inches on the drawing corresponds to just 1 foot in reality, which would suggest an impractically large scale drawing. It contradicts the given data, as the scale would not effectively represent the truck's actual length.
The scale of 1 inch = 6 feet accurately conveys the proportional relationship between the truck's scale drawing and its actual dimensions. By converting the truck's total length from feet to inches, we verify that 3 inches on the drawing equates to the correct actual length of 18 feet. The incorrect choices either misinterpret the scale or misrepresent the actual length, confirming that option C is the only valid scale representation.
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