Question 1132871
There is an original triangle with perimeter 80 cm
There are now two triangles, which together have the same perimeter as the original triangle AND also have a side not present in the original triangle, which is the altitude.  Each of them has this altitude.
The total perimeter of the two triangles is 140 cm, and they differ from the original triangle by two altitudes, one in each.  Therefore, the 60 cm increase is divided into two altitudes.
Each altitude is 30 cm., and that is the height of the original triangle.