Question

No triângulo retângulo a seguir, determine a medida desconhecida x:

Answer 1

$\large\textsf{Vamos L\'a:}$

$\boxed{\large\textbf{Teorema de Pit\'agoras.}}$
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$\large\textsf{F\'ormula do Teorema de Pit\'agoras::}$

$\medium\textsf{Considerando: "a" e "b" = Catetos ; "c" = Hipotenusa}$
$\mathsf{a^2+b^2 = c^2}$
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$\large\textsf{Aplicando o "Teorema de Pit\'agoras":}$

$\large\mathsf{a^2+b^2 = c^2}$
$\large\mathsf{(x+3)^2+3^2 = (x+4)^2}$

$\large\textsf{Vamos resolver separadamente os produtos not\'aveis:} \\\ \textsf{"quadrado da soma de dois termos"}$
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$(x+3)^2 \\\ x^2 +(2*x*3)+3^2 \\\ x^2+6x+3^2 \\\\\boxed{ = x^2+6x+9}$
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$(x+4)^2 \\\ x^2+(2*x*4)+4^2 \\\ x^2 + 8x + 4^2 \\\\\boxed{ = x^2+8x+16}$
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$\large\textsf{Prosseguindo:}$

$\large\mathsf{(x+3)^2+3^2 = (x+4)^2}$
$(x^2+6x+9) + 9 = (x^2+8x+16)$
$x^2+6x+9 + 9 = x^2+8x+16$
$x^2+6x+18 = x^2+8x+16$
$x^2+6x-x^2-8x =+16-18$
$+6x-8x =+16-18$
$-2x = -2$

$x = (-2):(-2)$

$\boxed{\large\textsf{x = 1}}$
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$\large\textbf{Resposta Final:}$

$\boxed{\large\textsf{x = 1}}$
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Bons Estudos!!!
;D