Use scale drawings and interpret scale factors. | Ratios, rates, proportional relationships, and units | SAT Math

核心知识

A scale factor is a ratio: $d r a w i n g m e a s u r e m e n t \times s c a l e f a c t o r = a c t u a l m e a s u r e m e n t$ . For areas, square the scale factor. For volumes, cube it.

深入理解

Scale drawing problems are proportion problems with one extra twist: the scale tells you the conversion factor.

If a blueprint says 1 inch = 8 feet, then every inch on paper represents 8 feet in reality. A wall that's 3.5 inches on the blueprint is $3.5 \times 8 = 28$ feet long.

Area scales differently. If lengths scale by factor $𝑘$ , areas scale by $𝑘 2$ . A room that's 2 in × 3 in on a 1 in : 8 ft blueprint has actual dimensions $16 𝑓 𝑡 \times 24 𝑓 𝑡$ , and actual area $16 \times 24 = 384 𝑓 𝑡 2$ — not $6 \times 8 = 48$ .

The SAT sometimes gives two different maps or blueprints at different scales and asks you to convert between them. Set up the proportion carefully: convert the drawing measurement to actual, then convert actual to the other drawing's scale.

分步讲解

Identify the scale (drawing : actual).
Set up the proportion: drawing/actual = scale drawing/scale actual.
For lengths, multiply by the scale factor directly.
For areas, multiply by the square of the scale factor.

常见误解

Using the linear scale factor for area calculations instead of squaring it.
Mixing up which direction the scale works — the drawing is always the smaller number.
Forgetting to convert all dimensions before computing area.

题目

示例解析

On a floor plan, 1 centimeter represents 2.5 meters. A rectangular room measures 4 cm by 6 cm on the floor plan. What is the actual area of the room, in square meters?

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