2.
a)
[tex] {h}^{2} + {2}^{2} = {3}^{2} \\ {h}^{2} + 4 = 9 \\ {h}^{2} = 5 \\ h = \sqrt{5} [/tex]
[tex]P = 7 \times \sqrt{5} = 7 \sqrt{5} [/tex]
b)
[tex] {h}^{2} + {3}^{2} = {4}^{2} \\ {h}^{2} + 9 = 16 \\ {h}^{2} = 7 \\ h = \sqrt{7} [/tex]
[tex]P = 7 \times \sqrt{7} = 7 \sqrt{7} [/tex]
3.
a)
[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} + 36 = 100 \\ {x}^{2} = 64 \\ x = \sqrt{64} \\ x = 8[/tex]
[tex]P = 6 \times 8 = 48[/tex]
b)
[tex]x = 5 \sqrt{2} [/tex]
[tex]P = 5 \sqrt{2} \times 5 = 25 \sqrt{2} [/tex]
4.
a)
[tex] {a}^{2} = {8}^{2} + {3}^{2} \\ {a}^{2} = 64 + 9 \\ {a}^{2} = 73 \\ a = \sqrt{73} cm[/tex]
Obwód
[tex]4 \times \sqrt{73} = 4 \sqrt{73} cm[/tex]
b)
[tex] {x}^{2} + (3x {)}^{2} = {20}^{2} \\ {x}^{2} + 9{x}^{2} = {20}^{2} \\ 10 {x}^{2} = 400 | \div 10 \\ {x}^{2} = 40 \\ x = \sqrt{40} \\ x = \sqrt{4 \times 10} \\ x = 2 \sqrt{10} cm[/tex]
[tex]3x = 3 \times 2 \sqrt{10} = 6 \sqrt{10} cm[/tex]
Obwód
[tex]2(x + 3x) = 2(2 \sqrt{10} + 6 \sqrt{10} ) = 2 \times 8 \sqrt{10} = 16 \sqrt{10} cm[/tex]
