Geometry and TrigonometryVery hardPerimeter of the midpoint triangle
Geometry and Trigonometry practice question
The midpoints of the three sides of a triangle with perimeter 36 are joined to form a smaller triangle. What is the perimeter of the smaller triangle?
Answer: 18
Each side of the smaller triangle is a midsegment — half the length of the side it is parallel to. So its perimeter is half of 36, which is 18.
Common wrong answers
- If you answered 9
- 9 is a quarter of 36; that is the ratio for AREAS of the two triangles, not perimeters.
- If you answered 12
- 12 is 36/3, the average side length of the original, not the smaller triangle's perimeter.
- If you answered 36
- The smaller triangle has half the perimeter, not the same.
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