1.
a)
[tex] {4}^{2} + {x}^{2} = {12}^{2} \\ 16 + {x}^{2} = 144 \\ {x}^{2} = 128 \\ x = \sqrt{128} \\ x = \sqrt{64 \times 2} \\ x = 8 \sqrt{2} [/tex]
b)
[tex](3 \sqrt{2} {)}^{2} + {x}^{2} = {6}^{2} \\ 9 \times 2 + {x}^{2} = 36 \\ 18 + {x}^{2} = 36 \\ {x}^{2} = 18 \\ x = \sqrt{18} \\ x = \sqrt{9 \times 2} \\ x = 3 \sqrt{2} [/tex]
c)
[tex] {6}^{2} + {3}^{2} = {x}^{2} \\ 36 + 9 = {x}^{2} \\ x = \sqrt{45} \\ x = \sqrt{9 \times 5} \\ x = 3 \sqrt{5} [/tex]
d)
[tex](2 \sqrt{5} {)}^{2} + {x}^{2} = (3 \sqrt{3} {)}^{2} \\ 4 \times 5 + {x}^{2} = 9 \times 3 \\ 20 + {x}^{2} = 27 \\ {x}^{2} = 7 \\ x = \sqrt{7} [/tex]
2.
[tex](2 \sqrt{6} {)}^{2} = {( \sqrt{3} )}^{2} + {x}^{2} \\ 4 \times 6 = 3 + {x}^{2} \\ 24 = 3 + {x}^{2} \\ {x}^{2} = 21 \\ x = \sqrt{21} [/tex]
3.
[tex](3 \sqrt{2} {)}^{2} + (4 \sqrt{3} {)}^{2} = {y}^{2} \\ 9 \times 2 + 16 \times 3 = {y}^{2} \\ 18 + 48 = {y}^{2} \\ {y}^{2} = 66 \\ y = \sqrt{66} [/tex]
4.
a)
[tex] {4}^{2} + {2}^{2} = {x}^{2} \\ 16 + 4 = {x}^{2} \\ 20 = {x}^{2} \\ x = \sqrt{20} \\ x = \sqrt{4 \times 5} \\ x = 2 \sqrt{5} [/tex]
NIE
b)
[tex] {0.3}^{2} + {0.4}^{2} = {x}^{2} \\ 0.09 + 0.16 = {x}^{2} \\ {x}^{2} = 0.25 \\ x = \sqrt{0.25} \\ x = 0.5[/tex]
TAK
c)
[tex](2 \sqrt{3} {)}^{2} + (4 \sqrt{2} {)}^{2} = {x}^{2} \\ 4 \times 3 + 16 \times 2 = {x}^{2} \\ 12 + 32 = {x}^{2} \\ x = \sqrt{44} \\ x = \sqrt{4 \times 11} \\ x = 2 \sqrt{11} [/tex]
NIE
d)
[tex]( { \sqrt{7} )}^{2} + ( \sqrt{5} {)}^{2} = {x}^{2} \\ 7 + 5 = {x}^{2} \\ 12 = {x}^{2} \\ x = \sqrt{12} \\ x = \sqrt{4 \times 3} \\ x = 2 \sqrt{3} [/tex]
TAK
5.
[tex]d = a \sqrt{2} \\ \\ d = 2 \sqrt{6} \times \sqrt{2} = 2 \sqrt{12} = 2 \sqrt{4 \times 3} = 2 \times 2 \sqrt{3} = 4 \sqrt{3} cm[/tex]
6.
[tex] \frac{a \sqrt{3} }{2} = \frac{3 \sqrt{3} }{2} | \times 2 \\ a \sqrt{3} = 3 \sqrt{3} | \div \sqrt{3} \\ a = 3[/tex]
Pole
[tex] \frac{ {3}^{2} \sqrt{3} }{4} = \frac{9 \sqrt{3} }{4} = 2.25 \sqrt{3} [/tex]
7.
[tex]h = \frac{a \sqrt{3} }{2} \\ \\ \\ h = \frac{6 \sqrt{3} }{2} = 3 \sqrt{3} cm[/tex]
