Question

1) aplicando o teorema de Pitágoras, determine a medida x indicada em cada um dos triângulos retângulos.

Answer 1

$(hipotenusa)^{2} =(cateto~1)^{2} +(cateto~2)^{2} \\ \\ a)\\ \\ x^{2} =21^{2}+28^{2}  \\ \\ x^{2} =441+784\\ \\ x^{2} =1225\\ \\ x=\sqrt{1225} \\ \\ x=35$

$b)\\ \\ x^{2} +24^{2} =25^{2} \\ \\ x^{2} =25^{2} -24^{2} \\ \\ x^{2} =625-576\\ \\ x^{2} =49\\ \\ x=\sqrt{49} \\ \\ x=7$

$c)\\ \\ x^{2} +5^{2} =11^{2} \\ \\ x^{2} =11^{2} -5^{2} \\ \\ x^{2} =121-25\\ \\ x^{2} =96\\ \\ x=\sqrt{96}$

$d)\\ \\ x^{2} =(\sqrt{10} )^{2} +(\sqrt{10} )^{2} \\ \\ x^{2} =10+10\\ \\ x=\sqrt{20}$

$e)\\ \\x^{2} +5^{2} =(\sqrt{29} )^{2} \\ \\ x^{2} +25=29\\ \\ x^{2} =29-25\\ \\ x^{2} =4\\ \\ x=\sqrt{4} \\ \\ x=2$

$f)\\ \\ x^{2} =24^{2} +32^{2}\\ \\ x^{2} =576+1024\\ \\ x^{2} =1600\\ \\ x=\sqrt{1600} \\ \\ x=40$

Answer 2

Resposta:

a)  x² = 28²+21²

x² = 784+441

x² = 1225

x = √12258

x = 35

B) 25² = x²+24²

    625 = x²+576

625-576 = x²

49 = x²

√49 = x

x = 7

C)11² = 5²+x²

121 = 25+x²

121-25 = x²

96 = x

√96 = √x²

√96 = x

D)x² = (√10)²+(√10)²

x² = 10+10

x² = 20

x = √20

x = 4,47

E)(√29)² = 5²+x²

     29 = 25+x²

     x² = 29-25

        x² = 4

         x² = √4

          x = 2

F)x² = 24²+32²

x² = 576+1,024

x² = 1,600

x = √1,600

x = 40

Explicação passo-a-passo: