Geometry and TrigonometryVery hardArea ratio of similar triangles
Geometry and Trigonometry practice question
Two triangles are similar, and the ratio of their corresponding side lengths is 2 : 5. The area of the smaller triangle is 12 square units. What is the area of the larger triangle, in square units?
Answer: 75
When lengths scale by 5/2, areas scale by (5/2)² = 25/4. So the larger area is 12 × 25/4 = 75.
Common wrong answers
- If you answered 30
- 30 scales the area by 5/2, the LENGTH ratio. Area is two-dimensional, so it scales by the square: 25/4.
- If you answered 60
- 60 doubles the length scaling (12 × 5) instead of squaring it: (5/2)² × 12 = 75.
- If you answered 7.5
- 7.5 scales the wrong way (12 × 5/8). The larger triangle has the larger area.
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