Odpowiedź:
zad 13
a)
a = √(2² + 2²) cm = √(4 + 4) cm = √(4 * 2) cm = 2√2 cm
g)
g√2 = 5 cm
g = 5/√2 cm = 5√2/2 cm = 2,5√2 cm
f)
f√2 = 8 cm
f = 8/√2 cm = 8√2/2 cm = 4√2 cm
zad 14
P - pole kwadratu = a² = 48 cm²
a² = 48 cm²
a = √48 cm = √(16 * 3) cm = 4√3 cm
d - przekątna kwadratu = a√2 = 4√3 cm * √2 = 4√(3 * 2) cm = 4√6 cm
zad 15
a)
IABI = IBCI = 10 [j]
IACI = IBCI * √2 = 10√2 [j]
Obwód = 2 * 10 + 10√2 = 20 + 10√2 = 10(2 + √2) [j]
P - pole trójkąta = 1/2 * IABI * IBCI = 1/2 * 10 * 10 = 5 * 10 = 50 [j²]
[j] - znaczy właściwa jednostka
b)
IBCI = IABI * √2 = 12 [j]
IABI = IBCI/√2 = 12/√2 = 12√2/2 = 6√2 [j]
IABI = IACI = 6√2 [j]
obwód = IABI + IACI + IBCI = 2 * 6√2 + 12 = 12√2 + 12 = 12(√2 + 1) [j]
P - pole trójkata = 1/2 * IABI * IACI = 1/2 * 6√2 * 6√2 =
= 3√2 * 6√2 = 18 * 2 = 36 [j²]
c)
IACI = IBCI
IABI = IACI * √2
IACI = IABI/√2 = 14/√2 = 14√2/2 = 7√2 [j]
obwód = IABI + IACI + IBCI = 14 + 7√2 + 7√2 = 14 + 14√2 = 14(1 + √2) [j]
P - pole trójkąta = 1/2 * IACI * IBCI = 1/2 * 7√2 * 7√2 = 49 * 2/2 = 49 [j²]
