A triangular pyramid is based on a triangle of sides $13$ cm, $14$ cm and $15$ cm; the other edges measure $ 1 $. Knowing the volume of the pyramid is $ 105 \sqrt {22} $ $ cm ^ 3 $, the value of $ l $, in cm, is equal to:
What I tried: I tried to calculate the perimeter to apply Herón's formula. So I found 84 in the area
HINT.
The foot of the height of the pyramid is the circumcenter of the base. Find height $h$ of the pyramid from volume and base area, then find circumradius $r$ of the base. You have then: $$ l=\sqrt{h^2+r^2}. $$