4·a + 4·s = 160 --> s = 40 - a
--------------------------------------------------
s2 = (a/2)2 + (a/2)2 + h2
(40 - a)2 = (a/2)2 + (a/2)2 + h2
h2 = 1/2·a2 - 80·a + 1600
--------------------------------------------------
V = 1/3·a2·h
V2 = 1/9·a4·h2
V2 = 1/9·a4·(1/2·a2 - 80·a + 1600)
V2 = 1/18·a4·(a2 - 160·a + 3200)
V2' = 1/9·a3·(3·a2 - 400·a + 6400) = 0 --> a = 18.59 cm
--------------------------------------------------
h = √(1/2·18.592 - 80·18.59 + 1600) = 16.89 cm