Geometry and TrigonometryVery hardPerimeter of a similar triangle from its longest side
Geometry and Trigonometry practice question
A triangle has sides of length 6, 9, and 12. A similar triangle has its longest side of length 20. What is the perimeter of the larger triangle?
Answer: 45
The scale factor is 20/12 = 5/3, and perimeters scale the same way: 27 × 5/3 = 45.
Common wrong answers
- If you answered 27
- 27 is the perimeter of the original triangle.
- If you answered 35
- 35 adds 8 to 27, the difference in the longest sides.
- If you answered 75
- 75 scales by 25/9, the ratio of areas.
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