Two similar triangles have linear scale factor 3:2. If the smaller triangle has area 32, what is the area of the larger triangle?

• A. 18
• B. 40
• C. 64
• D. 72

Answer: (D)

The main idea here is that the area of similar figures changes by the square of the linear scale factor. The larger triangle is bigger by a linear factor of 3/2 relative to the smaller one. Squaring that factor gives (3/2)² = 9/4, so the area scales by 9/4. Multiply the smaller area by 9/4: 32 × 9/4 = 32 × 2.25 = 72. Therefore, the larger triangle’s area is 72.