Use the technique completion of the square to factorise x^2 + 2 (1 - p)x + p(p - 2)

The pyraminx is a rubik's cube-type toy in the shape of a tetrahedron. the pyraminx shown below has edges 15\,\text{cm}15cm long and vertical height h=12.2\,\text{cm}h=12.2cm. the triangle drawn with dashed lines is a right triangle. what is the distance rr? round your answer to the nearest tenth.