Problem 8 · 2012 Math Kangaroo
Medium
Geometry & Measurement
pythagorean-tripleperimeter
ABC is a right-angled triangle with shorter sides 6 cm and 8 cm. K, L, M are the midpoints of the sides of triangle ABC. What is the perimeter of triangle KLM?
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Answer: B — 12 cm
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Hint 1 of 2
First find the third side of the 6–8 right triangle.
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Hint 2 of 2
The triangle joining the midpoints has sides exactly half of the original.
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Approach: medial triangle has half the perimeter
- The right triangle has legs 6 and 8, so its hypotenuse is 10 and its perimeter is 24.
- Joining the midpoints of the sides makes the medial triangle, whose sides are half as long.
- So its perimeter is half of 24, which is 12 cm (B).
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