Two heights of a scalene triangle measure 8 and 3. Find the third height of this triangle given it is also an integer

Answer 1

if 8 and 3 are heights

then let the bases = 3 and 8, with area = 12

3rd side would be between 5 and 11

integers would be 6, 7 8, 9 or 10

but scalene eliminates 6 and 7

to get area of 12 narrows it down to 8 for 3rd side

which corresponds to height of 3

sides are 3, 8 and 8

heights are 8, 3 and 3