A rectangular blueprint uses a 1:500 scale. If plan dimensions are 30 cm by 20 cm, determine the actual area.
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Answer: D. 15000 m²
Explanation
A scale factor of one to five hundred means plan dimensions must be multiplied by five hundred. Converting plan dimensions of thirty and twenty centimeters yields actual dimensions of one hundred fifty and one hundred meters. Multiplying the actual length by breadth gives a total area of fifteen thousand square meters. Architectural blueprints use scale ratios to represent large physical structures on paper. Linear scale factors must be squared when calculating two dimensional surface areas from plans. Metric conversions change centimeters to meters before computing final land areas.
Civil engineers and architects rely on scaled blueprints to estimate material and land requirements. Urban planning requires accurate translation of map dimensions into real world square footage. Scale factor problems connect ratio mathematics with practical engineering design work. Option a underestimates the actual area by failing to apply the squared scale factor correctly. Option b suggests fifteen hundred square meters which results from an incorrect unit conversion. Option c proposes twelve thousand square meters due to an arithmetic error in dimension scaling.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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