Difference between revisions of "2008 AMC 10B Problems/Problem 7"
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− | The area of the large triangle is <math>\frac{10^2\sqrt3}{4}</math>, while the area each small triangle is <math>\frac{1^2\sqrt3}{4}</math>. Dividing these two quantities, we get 100, therefore 100 small triangles can fit in the large one. | + | The area of the large triangle is <math>\frac{10^2\sqrt3}{4}</math>, while the area each small triangle is <math>\frac{1^2\sqrt3}{4}</math>. Dividing these two quantities, we get 100, therefore <math>\boxed{100}</math> small triangles can fit in the large one. |
Revision as of 12:31, 14 February 2009
Problem
An equilateral triangle of side length is completely filled in by non-overlapping equilateral triangles of side length . How many small triangles are required?
Solution
The area of the large triangle is , while the area each small triangle is . Dividing these two quantities, we get 100, therefore small triangles can fit in the large one.
Another Solution:
The number of triangles is .
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |