2008 AMC 10B Problem 7

Below is the professionally curated solution for Problem 7 of the 2008 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10B solutions, or check the answer key.

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

Difficulty rating: 880

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?

$10$

$25$

$100$

$250$

$1000$

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.

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