Odpowiedź:
1
a) 5cm +5cm<11cm
5cm+11cm >5cm
5cm+11cm>5cm
nie
b) 3xm+3cm >1cm
3cm+1cm>3cm
3cm+1cm>3cm
tak
c) 2cm+2cm<20cm
2cm+20cm>2cm
2cm+20cm>2cm
2
[tex] {8}^{2} + {15}^{2} = {x}^{2} \\ 64 + 225 = {x}^{2} \\ 289 = {x}^{2} \\ x = \sqrt{289} \\ x = 17[/tex]
[tex] {2}^{2} + {y}^{2} = {5}^{2} \\ 4 + {y}^{2} = 25 \\ {y}^{2} = 25 - 4 \\ {y}^{2} = 21 \\ y = \sqrt{21} [/tex]
[tex] {z}^{2} + ( { \sqrt{5} })^{2} = {(2 \sqrt{2} })^{2} \\ {z}^{2} + 5 = 8 \\ {z}^{2} = 8 - 5 \\ z^{2} = 3 \\ z = \sqrt{3} [/tex]
3
[tex] {8}^{2} + {100}^{2} = {x}^{2} \\ 64 + 100 = {x}^{2} \\ {x}^{2} = 164 \\ x = \sqrt{164} \\ x = 2 \sqrt{41} [/tex]
4
wysokosc
[tex] {3}^{2} + {x}^{2} = {5}^{2} \\ 9 + {x}^{2} = 25 \\ {x}^{2} = 25 - 9 \\ {x}^{2} = 16 \\ x = \sqrt{16} \\ x = 4[/tex]
pole
[tex] \frac{(10 + 4) \times 4 }{2} = \frac{14 \times 4}{2} = 7 \times 4 = 28[/tex]
5
[tex] {5}^{2} + {x}^{2} = 13^{2} \\ 25 + {x}^{2} = 169 \\ {x}^{2} = 169 - 25 \\ {x}^{2} = 144 \\ x = \sqrt{144} \\ x = 12[/tex]
2 przekątna=24
pole
[tex] \frac{10 \times 24}{2} = 10 \times 12 = 120[/tex]
