Racso ⇒ 76 Tópico resolvido

[petras]

Problema Proposto
31 - Sobre uma reta se marcam os pontos consecutivos A, B, C e D
de modo que [tex3]\frac{AB}{AD}=\frac{BC}{CD}[/tex3] e 36CD= 5AB
Se BC= 8, calcular AD.

Resposta

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D) 90

[petras]

[tex3]\mathsf{
CD = x\\
AB = \frac{36x}{5}\\
BC = 8\\
AD = \frac{36x}{5}+8+x = \frac{41x+40}{5}\\
\therefore \frac{\frac{36x}{5}} {\frac{41x+40}{5}}=\frac{8}{x} \implies 9x^2-82x-80=0\\
\therefore x =10 \implies \boxed{\color{red}AD = \frac{360}{5}+8+10 = 90}






}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{
CD = x\\
AB = \frac{36x}{5}\\
BC = 8\\
AD = \frac{36x}{5}+8+x = \frac{41x+40}{5}\\
\therefore \frac{\frac{36x}{5}} {\frac{41x+40}{5}}=\frac{8}{x} \implies 9x^2-82x-80=0\\
\therefore x =10 \implies \boxed{\color{red}AD = \frac{360}{5}+8+10 = 90}






}[/tex3]