Question

Por favor me ajudem essa !

Answer 1

$a) \\ {a}^{2} = {b}^{2} + {c}^{2} \\ {20}^{2} = ({4x})^{2} + ({3x})^{2} \\ 400 = 16 {x}^{2} + 9 {x}^{2} \\ 400 = 25 {x}^{2} \\ 25 {x}^{2} = 400 \\ {x}^{2} = \frac{400}{25} \\ {x}^{2} = 16 \\ x = \sqrt{16} \\ x = - 4 \: e \: 4 \\ \\ b) \\ {a}^{2} = {b}^{2} + {c}^{2} \: \\ ( {3 \sqrt{5} })^{2} = {6}^{2} + {x}^{2} \\ 9 \times 5 = 36 + {x}^{2} \\ 45 = 36 + {x}^{2} \\ {x}^{2} + 36 = 45 \\ {x}^{2} = 45 - 36 \\ {x}^{2} = 9 \\ x = \sqrt{9} \\ x = - 3 \: e \: 3 \\ \\ c) \\ {a}^{2} = {b}^{2} + {c}^{2} \\ {(x + 1)}^{2} = {x}^{2} + {( \sqrt{7} })^{2} \\ {x}^{2} + 2 \times x \times 1 + {1}^{2} = {x}^{2} + 7 \\ {x}^{2} + 2x + 1 - {x}^{2} = 7 \\ 2x = 7 - 1 \\ 2x = 6 \\ x = \frac{6}{2} \\ x = 3 \\ \\ d) \\ {a}^{2} = {b}^{2} + {c}^{2} \\ {(3 \sqrt{2}) }^{2} = {x}^{2} + {x}^{2} \\ 9 \times 2 = 2x \\ 2x = 18 \\ x = \frac{18}{2} \\ x = 9$