A red equilateral triangle $T$ with side length $1$ is drawn on a plane. For a positive real $c$, we place three blue equilateral triangle shaped paper with side length $c$ on a plane to cover $T$ completely. Find the minimum value of $c$. As shown in the picture, it doesn't matter if the blue papers overlap each other or stick out from $T$. Folding or tearing the paper is not allowed.
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