Question

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Answer 1

Resposta:

Explicação passo a passo:

$1) a) x^{2} = 5^{2} + 12^{2} \\ x^{2} = 25 + 144\\ x^{2} = 169\\ x = \sqrt{169} \\ x = 13$

$b) 7,5^{2} = x^{2} + 4,5^{2} \\ 56,25 = x^{2} + 20,25\\ x^{2} + 20,25 = 56,25\\ x^{2} = 56,25 - 20,25\\ x^{2} = 36\\ x = \sqrt{36} \\ x = 6$

$c) 20^{2} = (4x)^{2} + (3x)^{2} \\ 400 = 16x^{2} + 9x^{2} \\ 400 = 25x^{2} \\ x^{2} = \frac{400}{25} \\ x^{2} = 16\\ x = \sqrt{16} \\ x = 4$

$2) x^{2} = 6^{2} + 8^{2} \\ x^{2} = 36 + 64\\ x^{2} = 100\\ x = \sqrt{100} \\ x = 10$

$3) 8^{2} = x^{2} + 15^{2} \\ 64 = x^{2} - 225 x^{2} - 225 = 64\\ x^{2} = 64 + 225\\ x^{2} = 289\\ x = \sqrt{289} \\ x = 17$

$4) 12^{2} = x^{2} - 16^{2} \\ 144 = x^{2} - 256\\ x^{2} - 256 = 144\\ x^{2} = 144 + 256\\ x^{2} = 400\\ x = \sqrt{400} \\ x = 20$

$5) x^{2} = 9^{2} + 12^{2} \\ x^{2} = 81 + 144\\ x^{2} = 225\\ x = \sqrt{225} \\ x = 15$