Question 94
Two incongruent triangles $ABC$ and $XYZ$ are called a pair of *pals* if they satisfy the following conditions:
(a) the two triangles have the same area;
(b) let $M$ and $W$ be the respective midpoints of sides $BC$ and $YZ$. The two sets of lengths $\{AB, AM, AC\}$ and $\{XY, XW, XZ\}$ are identical 3-element sets of pairwise relatively prime integers.
Determine if there are infinitely many pairs of triangles that are pals of each other.
(a) the two triangles have the same area;
(b) let $M$ and $W$ be the respective midpoints of sides $BC$ and $YZ$. The two sets of lengths $\{AB, AM, AC\}$ and $\{XY, XW, XZ\}$ are identical 3-element sets of pairwise relatively prime integers.
Determine if there are infinitely many pairs of triangles that are pals of each other.