Odpowiedź:
zad 1
a - bok trójkąta
h - wysokość = a√3/2 = a - 1 cm
a√3/2 = a - 1 cm
a√3 =2(a - 1 cm)
a√3 = 2a - 2 cm
a√3 - 2a = - 2 cm
a(√3 - 2) = - 2 cm
a = - 2/(√3 - 2) cm = - 2(√3 + 2)/(3 - 4) cm = - 2(√3 + 2)/(- 1) = 2(√3 + 2) cm
P - pole trójkąta = a²√3/4 = [2(√3 + 2)² * √3]/4 cm²=
= [4(3 + 4√3 + 4] * √3/4 cm² = (12 + 16√3 + 16) * √3/4 cm² =
= (28 + 16√3) * √3/4 cm² = ( 28√3 + 16 * 3)/4 cm² = (28√3 + 48)/4 cm² =
= (7√3 + 12 ) cm²
zad 2
a - bok kwadratu
d - przekątna = a√2 = a + 1 cm
a√2 = a + 1 cm
a√2 - a = 1 cm
a(√2 - 1) = 1 cm
a = 1/(√2 - 1) cm = (√2 + 1)/(2 - 1) cm = (√2 + 1)/1 cm = (√2 + 1) cm
P - pole kwadratu = a² = (√2 + 1)² cm² = (2 + 2√2 + 1) cm² = (3 + 2√2) cm²
