Korzystamy z twierdzenia Pitagorasa
a)
Najpierw obliczmy bok danego kwadratu
[tex] {a}^{2} = 225 \\ a = 15[/tex]
Zatem obliczmy bok szukanego kwadratu
[tex] {15}^{2} = {9}^{2} + {x}^{2} \\ 225 = 81 + {x}^{2} \\ {x}^{2} = 144 \\ x = \sqrt{144} = 12[/tex]
Zatem pole tego kwadratu
[tex]12 \times 12 = 144[/tex]
b)
Najpierw obliczmy bok danego kwadratu
[tex] {a}^{2} = 300 \\ a = 10 \sqrt{3} [/tex]
Zatem obliczmy bok szukanego kwadratu
[tex] {20}^{2} = {x}^{2} + {(10 \sqrt{3}) }^{2} \\ 400 = {x}^{2} + 100 \times 3 \\ 400 = {x}^{2} + 300 \\ {x}^{2} = 100 \\ x = \sqrt{100} = 10[/tex]
Zatem pole tego kwadratu
[tex]10 \times 10 = 100[/tex]
