Let $T\subset \mathbb{R}^2$ be any triangle and $T^t$ a deformation of $T$. Call $l_1,l_2,l_3$ the squares of the lengths of the sides of $T$ and $l_1^t,l_2^t,l_3^t$ the squares of the lengths of the corresponding sides of $T^t$. Let $\phi_t:T\rightarrow T^t$ be the affine map which sends sides to corresponding sides.

This is the problem I'd like to solve:

**Find triangles $T$ such that the following equality is verified for any deformation $T^t$:**
$$Max\{\frac{l_1}{l_1^t},\frac{l_2}{l_2^t},\frac{l_3}{l_3^t}\}=Lip(\phi_t)^2$$

where $Lip(\phi_t)$ is the Lipschitz constant of $\phi_t$.