Among three rods, the first two are made of same material having coefficient of linear expansion `alpha_1` and the third rod is made of material of coefficient of linear expansion `alpha_2` . The third rod forms the base of the equilateral triangle when the three rods are arranged to form an equilateral triangle. If the altitude of triangle remains constant at all temperatures, what is the ratio of `alpha_1//alpha_2` ?

Explanation

To solve the problem, we need to find the ratio of the coefficients of linear expansion \( \frac{\alpha_1}{\alpha_2} \) given that the altitude of the equilateral triangle formed by the three rods remains constant at all temperatures.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have three rods arranged to form an equilateral triangle.
- The first two rods (AB and AC) are made of the same material with coefficient of linear expansion \( \alpha_1 \).
- The third rod (BC) is made of a different material with coefficient of linear expansion \( \alpha_2 \).
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