In an architect's scale drawing, the length of a kitchen is 4.5 centimeters. The actual length of the kitchen is 15 feet. If the width of the kitchen in the scale drawing is 2.7 centimeters, what is the actual width of the kitchen?
The actual width of the kitchen is 9.0 feet.
To determine the actual width of the kitchen, we first calculate the scale factor from the scale drawing. Given that 4.5 centimeters corresponds to 15 feet, the scale factor is 15 feet / 4.5 centimeters = 3.33 feet per centimeter. Thus, multiplying the width in the drawing (2.7 centimeters) by the scale factor gives us the actual width of 9.0 feet.
This choice results from incorrectly calculating the scale factor or not properly applying it to the width. If one mistakenly assumes the scale is lower than it is, the resulting width will be underestimated, leading to an incorrect conclusion.
This is the correct answer, as it accurately reflects the calculated actual width derived from the scale drawing dimensions. By applying the previously determined scale factor of 3.33 feet per centimeter to the width of 2.7 centimeters, the calculation yields 2.7 cm * 3.33 ft/cm = 9.0 feet.
This option suggests an overestimation of the width due to a miscalculation of the scale factor or failure to convert centimeters to feet correctly. Such errors typically arise from incorrect multiplication or misunderstanding of the scale relationship.
Choosing this figure indicates a significant miscalculation, possibly by incorrectly multiplying the width in centimeters by an inflated or incorrect scale factor. This reflects a misunderstanding of the relationship between the drawing dimensions and actual measurements.
In conclusion, the accurate conversion of dimensions from a scale drawing to actual measurements relies heavily on understanding the scale factor. The width of the kitchen in the scale drawing of 2.7 centimeters correctly translates to an actual width of 9.0 feet when the scale factor is applied properly. Understanding these calculations is crucial for accurate architectural and design work.
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