Odpowiedź:
a)
h/5 = 1/2 /*5
h = 2,5 j
5^2 = 2,5^2 + x ^2
25 = 25/5 + x^2
x^2 = 18,75
x = 2,5[tex]\sqrt{3}[/tex] j
2,5/b = [tex]\sqrt{2} /2[/tex] /*b
[tex]\sqrt{2} /2[/tex]b = 2,5 /
b = 5/√2 = 2,5√2 j
(5/√2)^2 = 2,5^2 + y ^2
25/2 = 25/4 + y^2
y^2 = 25/4
y = 5/2 j
Obwód = 2,5√3 + 2,5√2 + 5 + 2,5 = 7,5 + 2,5√3 + 2,5√2 j
Pole = (2,5 + 2,5[tex]\sqrt{3}[/tex]) * 2,5 * 0,5 = (25 + 25√3)/8 j^2
b)
h/4 = √3/2 /*4
h = 2√3 j
6^2 = (2√3)^2 + x^2
36 = 12 + x^2
X^2 = 24
x = 2√6 j
2√3/c = 1/2 /*c
1/2c = 2√3
c = 4√3 j
(4√3)^2 = (2√3)^2 + y ^2
48 = 12 + y^2
y^2 = 36
y = 6 j
P = 0.5 * (6+2√6) * 2√3 = (3+√6) * 2√3 = 6√3 + 6√2 j^2
Obwód = 6 + 4√3 +6 + 2√6 = 12 + 4√3 + 2√6 j
c)
√3/c = 1/2 /*c
√3 = 1/2c
c = 2√3 j
(2√3 )^2 = √3^2 + a^2
12 = 3 + a^2
a^2 = 9
a = 3 j
Obwód = 9 + 2√3 + √3 = 9 + 3√3 j
P = √3 * 0.5 * 3 = 1,5√3 j^2
d)
h/4 = √3/2 /*h
h = 2√3
4^2 = (2√3)^2 + x^2
16 = 12 + x^2
X^2 = 4
x = 2 j
2√3/c = √2/2 /*c
√2/2c = 2√3 /√2/2
c = 2√6 j
(2√6)^2 = (2√3)^2 + y^2
24 = 12 + y^2
y^2 = 12
y = 2√3 j
Obwód = 2√6 + 2 + 2√3 + 4 = 6 + 2√6 + 2√3 j
Pole = 0.5 * 2√3 * (2+2√3) = 6 + 2√3 j^2
e)
5√3/h = 3/√3 /*h
5√3 = 3/√3 h / 3/√3
h = 5 j
c^2 = 5^2 + (5√3)^2
c^2 = 25 + 75
c^2 = 100
c = 10 j
5/b = √2/2 /*b
√2/2b = 5 /√2/2
b = 10/√2 = 5√2 j
(5√2)^2 = 25 + y^2
y^2 = 50 - 25 = 25 /√
y = 5 j
Obwód = 10 + 5√2 + 5 + 5√3 = 15 + 5√2 + 5√3 cm
Pole = 0.5 * 5 * (5√3 + 5) = 12,5 + 12,5√3 cm^2
f)
h/4√2 = √2/2 /*4√2
h = 4 j
4/c = 1/2 /*c
1/2c = 4 /*2
c = 8 j
(4√2)2 = 4^2 + x^2
32 = 16+ x^2
x^2 = 16
x = 4 j
8^2 = 4^2 + y^2
64 = 16 + y62
y^2 = 64 - 16 = 48 /√
y = 4√3 j
Obwód = 4√2 + 8 + 4 + 4√3 = 12 + 4√2 + 4√3 j
Pole = 0.5 * 4 * (4+4√3) = 8 + 8√3 j^2
