Utilizando o Teorema de Pitágoras, determine o valor de x nos triângulos abaixo:
Hipotenusa: 20 e Catetos: 3x e 4x
Hipotenusa: 3 Raiz de 5 Catetos: x e 6
Hipotenusa: x + 1 Catetos: Raiz de 7 e x
Hipotenusa: 3 Raiz de 2 Catetos: x e x
Soluções para a tarefa
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Teorema de Pity:
![Hipoteusa^2= cateto^2+cateto^2 Hipoteusa^2= cateto^2+cateto^2](https://tex.z-dn.net/?f=Hipoteusa%5E2%3D+cateto%5E2%2Bcateto%5E2)
Hipotenusa: 20 e Catetos: 3x e 4x
![20^2=(3x)^2+(4x)^2\\400=9x^2+16x^2
\\400=25x^2\\x^2= \frac{400}{25}= \frac{4*100}{25}=4* \frac{100}{25}=4*4
\\x^2=16\\x= \sqrt{16}\\x=4 20^2=(3x)^2+(4x)^2\\400=9x^2+16x^2
\\400=25x^2\\x^2= \frac{400}{25}= \frac{4*100}{25}=4* \frac{100}{25}=4*4
\\x^2=16\\x= \sqrt{16}\\x=4](https://tex.z-dn.net/?f=20%5E2%3D%283x%29%5E2%2B%284x%29%5E2%5C%5C400%3D9x%5E2%2B16x%5E2%0A%5C%5C400%3D25x%5E2%5C%5Cx%5E2%3D+%5Cfrac%7B400%7D%7B25%7D%3D+%5Cfrac%7B4%2A100%7D%7B25%7D%3D4%2A+%5Cfrac%7B100%7D%7B25%7D%3D4%2A4%0A%5C%5Cx%5E2%3D16%5C%5Cx%3D+%5Csqrt%7B16%7D%5C%5Cx%3D4++++)
Hipotenusa: 3 Raiz de 5 Catetos: x e 6
![(3 \sqrt{5})^2=x^2+6^2\\
3^2 *( \sqrt{5})^2=x^2+36
\\9*5=x^2+36\\45=x^2+36\\x^2=45-36 \\x^2=9\\x= \sqrt{9}
\\x=3 (3 \sqrt{5})^2=x^2+6^2\\
3^2 *( \sqrt{5})^2=x^2+36
\\9*5=x^2+36\\45=x^2+36\\x^2=45-36 \\x^2=9\\x= \sqrt{9}
\\x=3](https://tex.z-dn.net/?f=%283+%5Csqrt%7B5%7D%29%5E2%3Dx%5E2%2B6%5E2%5C%5C%0A3%5E2+%2A%28+%5Csqrt%7B5%7D%29%5E2%3Dx%5E2%2B36%0A%5C%5C9%2A5%3Dx%5E2%2B36%5C%5C45%3Dx%5E2%2B36%5C%5Cx%5E2%3D45-36+%5C%5Cx%5E2%3D9%5C%5Cx%3D+%5Csqrt%7B9%7D%0A%5C%5Cx%3D3)
Hipotenusa: x + 1 Catetos: Raiz de 7 e x
![(x+1)^2= (\sqrt{7}) ^2+x^2
\\x^2+2x+1=7+x^2\\x^2+2x+1-x^2=7\\2x+1=7\\2x=7-1\\2x=6\\x= \frac{6}{2}=3 \\x=3 (x+1)^2= (\sqrt{7}) ^2+x^2
\\x^2+2x+1=7+x^2\\x^2+2x+1-x^2=7\\2x+1=7\\2x=7-1\\2x=6\\x= \frac{6}{2}=3 \\x=3](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%3D+%28%5Csqrt%7B7%7D%29+%5E2%2Bx%5E2%0A%5C%5Cx%5E2%2B2x%2B1%3D7%2Bx%5E2%5C%5Cx%5E2%2B2x%2B1-x%5E2%3D7%5C%5C2x%2B1%3D7%5C%5C2x%3D7-1%5C%5C2x%3D6%5C%5Cx%3D+%5Cfrac%7B6%7D%7B2%7D%3D3+%5C%5Cx%3D3)
Obs.:
é um produto notável chamado de quadrado da soma
Hipotenusa: 3 Raiz de 2 Catetos: x e x
![(3 \sqrt{2})^2=x^2+x^2\\3^2* (\sqrt{2})^2 =2x^2\\9*2=2x^2\\x^2= \frac{9*2}{2}\\x^2=9\\x= \sqrt{9} \\x=3 (3 \sqrt{2})^2=x^2+x^2\\3^2* (\sqrt{2})^2 =2x^2\\9*2=2x^2\\x^2= \frac{9*2}{2}\\x^2=9\\x= \sqrt{9} \\x=3](https://tex.z-dn.net/?f=%283+%5Csqrt%7B2%7D%29%5E2%3Dx%5E2%2Bx%5E2%5C%5C3%5E2%2A+%28%5Csqrt%7B2%7D%29%5E2++%3D2x%5E2%5C%5C9%2A2%3D2x%5E2%5C%5Cx%5E2%3D+%5Cfrac%7B9%2A2%7D%7B2%7D%5C%5Cx%5E2%3D9%5C%5Cx%3D+%5Csqrt%7B9%7D+%5C%5Cx%3D3+)
Espero ter ajudado ^^
Hipotenusa: 20 e Catetos: 3x e 4x
Hipotenusa: 3 Raiz de 5 Catetos: x e 6
Hipotenusa: x + 1 Catetos: Raiz de 7 e x
Obs.:
Hipotenusa: 3 Raiz de 2 Catetos: x e x
Espero ter ajudado ^^
mahsantos3:
Muito obrigada <3
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