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Geometry and Trigonometry Difficulty: Hard

The floor of a ballroom has an area of $600$ square meters. An architect creates a scale model of the floor of the ballroom, where the length of each side of the model is $\frac{1}{10}$ times the length of the corresponding side of the actual floor of the ballroom. What is the area, in square meters, of the scale model?

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Explanation

Choice A is correct. It’s given that the length of each side of a scale model is $\frac{1}{10}$ times the length of the corresponding side of the actual floor of a ballroom. Therefore, the area of the scale model is ${(\frac{1}{10})}^{2}$ , or $StartFraction 1 Over 100 EndFraction$ , times the area of the actual floor of the ballroom. It’s given that the area of the floor of the ballroom is $600$ square meters. Therefore, the area, in square meters, of the scale model is $left parenthesis StartFraction 1 Over 100 EndFraction right parenthesis left parenthesis 600 right parenthesis$ , or $6$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.