16Hit1600
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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