2008 AMC 10B Problem 7

Problem 7 of 25EasierGeometry

An equilateral triangle of side length

10

is completely filled in by non-overlapping equilateral triangles of side length

1.

How many small triangles are required?

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Solution

The large triangle has side length

10

times that of a small triangle, so its area is

10^2=100

times as large. Since the small triangles tile it without overlap, exactly

100

of them are required. Thus, the correct answer is C.

Concepts: power scaling of length, area, and volume · equilateral triangle

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.