Geometry and TrigonometryHardPerimeter of a similar triangle
Geometry and Trigonometry practice question
Triangle ABC has sides of length 5, 6, and 10. Triangle DEF is similar to triangle ABC, and its longest side has length 25. What is the perimeter of triangle DEF?
Answer: 52.5 or 105/2
The scale factor is 25/10 = 2.5. Perimeters scale the same way: (5 + 6 + 10) × 2.5 = 21 × 2.5 = 52.5.
Common wrong answers
- If you answered 21
- 21 is the perimeter of triangle ABC.
- If you answered 36
- 36 adds 15 to the perimeter (the increase of the longest side), but similarity scales, it doesn't add.
- If you answered 131.25
- 131.25 scales the perimeter by 2.5² — that's how AREAS scale, not perimeters.
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