An architect builds a scale model of a house in which 1 inch... | SAT Ratios, rates, proportional relationships, and units Question, Answer Explained

Question bank / Ratios, rates, proportional relationships, and units

Math · Problem-Solving and Data AnalysisHard

An architect builds a scale model of a house in which $1$ inch represents $8$ feet. The floor of the model has an area of $45$ square inches. What is the area, in square feet, of the floor of the actual house?

$360$

$720$

$2{,}880$

$23{,}040$

Show answer and explanation

Answer: C

Each inch on the model represents $8$ feet, so each square inch represents $8 \times 8 = 64$ square feet. The actual floor area is $45 \times 64 = 2{,}880$ square feet.

Choice A multiplies by the linear scale factor, $8$ , but areas scale by the square of the linear scale factor.

Why the other choices are wrong

A. This multiplies 45 by 8, but area scales by the square of the scale factor, 64.
B. This multiplies by 8 + 8 = 16. Each square inch represents 8 × 8 = 64 square feet.
D. This multiplies by 8 cubed, 512, which is how volume scales, not area.

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