If two similar triangles have a linear scale factor of 3 from triangle A to triangle B, what is the scale factor for their areas?

• A. 1/9
• B. 3
• C. 9
• D. 27

Answer: (C)

Areas scale with the square of the linear scale factor. If corresponding linear dimensions are multiplied by 3, each dimension grows by 3 and the area grows by 3 × 3, which is 9. So the scale factor for areas is 9. For example, if triangle A has area 1, triangle B would have area 9. The other options don’t fit: 1/9 would mean shrinking by 1/3, 3 would be the length factor itself, not the area factor, and 27 would be using a cube of the factor, which isn’t how area scales.