# Equilateral Triangles using Matchsticks

You are given an equilateral triangle of three matchsticks like given figure. What is the minimum number of sticks needed to add three more equilateral triangles to it?

**Given equilateral triangle:**

**Answer :** 3

**Solution:** Below are the different methods to approach this problem.

**Approach-1:** A tetrahedron (a three-sided pyramid). An additional three matches will be needed in the existing triangle to make it.

**Approach-2: **As one** **equilateral triangle is already there and 3 more are needed so in total 4 equilateral triangles are needed of a given size, so by adding 3 more matchsticks like below, 4 equilateral triangles can be formed.

Thanks to Palak Gupta for adding approach 2.

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