P = 18 √6
a/b = 2/5
więc przyjmuję:
a = 2x
b = 5x
z tw. pit. licze wysokość:
b² = (1/2a)² + h²
25x² = x² + h²
h² = 24x²
h = x √24
h = 2x √6
z pola:
½ * a*h = 18 √6
½ * 2x * 2x √6 = 18 √6
2 x² √6 = 18 √6
x² = 9
x = 3
a = 2*3 = 6
h= 2*3*√6 = 6√6
b = 5*3 = 15
P = ½ * b * H
½ * 15 * H = 18 √6
H = 2,4 √6
odp. h = 6√6 i dwie wysokości H = 2,4 √6
