there is likely a countably infinity of real solutions?
however, if you simply stay with integer solutions
clearly, there is no "square" solution
for a rectangle of height H and breadth B and perimeter P
H = ((P- (2 * B))/2) where here P = constant = 78
eg
B ... Rectangle ... P
1 ... (1 x 38) ... 78
2 ... (2 x 37) ... 78
3 ... (3 x 36) ... 78
4 ... (4 x 35) ... 78
and so on ...
+40 
