Geometry and TrigonometryMediumPerimeter of a similar triangle
Geometry and Trigonometry practice question
A triangle has side lengths 3, 4 and 5. A second triangle is similar to it, and the shortest side of the second triangle has length 9. What is the perimeter of the second triangle?
Answer: 36
The shortest sides correspond: 9 / 3 = 3, so every side of the second triangle is 3 times the matching side of the first. Its sides are 9, 12 and 15, and the perimeter is 36. (Or: perimeters scale by the same factor, 12 × 3 = 36.)
Common wrong answers
- If you answered 12
- 12 is the perimeter of the ORIGINAL triangle, 3 + 4 + 5. The second triangle is three times larger.
- If you answered 15
- 15 is only the longest side of the second triangle (5 × 3). The perimeter adds all three.
- If you answered 27
- 27 is 3 × 9, tripling just the shortest side. All three sides scale, then they're added: 9 + 12 + 15.
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