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Triangle Problem

Author:
J Wilson

What do you notice when you move the vertices of the larger triangle?

What is the area of the smaller triangle as a fraction of the larger triangle when each vertex of the larger triangle is connected to a point (1/3)rd of the way along the opposite edge? (Try calculating for an equilateral triangle). What is the area of the smaller triangle as a fraction of the larger triangle when each vertex of the larger triangle is connected to a point (1/n)th of the way along the opposite edge? How could you extend this for (k/n)?