1. A plank of wood has one end, $A$, against a vertical wall. Its other end, $B$, is on horizontal ground. When end $A$ slips down $8 \mathrm{~cm}$, end $B$ moves $4 \mathrm{~cm}$ further away from the wall. When end $A$ slips down a further $9 \mathrm{~cm}$, end $B$ moves a further $3 \mathrm{~cm}$ away from the wall. Find the length of the plank.