2003 AMC 10A Problems/Problem 23
Problem
A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have rows of small congruent equilateral triangles, with small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of small equilateral triangles?
Solution
There are small equilateral triangles.
Each small equilateral triangle needs toothpicks to make it.
But, each toothpick that isn't one of the toothpicks on the outside of the large equilateral triangle is a side for small equilateral triangles.
So, the number of toothpicks on the inside of the large equilateral triangle is
Therefore the total number of toothpicks is