Question

me ajudem pfvorrr
Na figura, temos que a//b//c. Considerando que
AB=6cm
AC=14cm
DE=12cm
Qual a medida de DF?​

Answer 1

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$\sf \overline{AB}+\overline{BC}=\overline{AC}\\\sf 6+\overline{BC}=14\\\sf\overline{BC}=14-6\\\sf\overline{BC}=8\\\sf\overline{DE}+\overline{EF}=\overline{DF}\\\sf12+\overline{EF}=\overline{DF}\implies\overline{EF}=\overline{DF}-12$

$\underline{\sf pelo~teorema~de~Tales~temos:}\\\sf\dfrac{\overline{AB}}{\overline{BC}}=\dfrac{\overline{DE}}{\overline{EF}}\\\sf\dfrac{6}{8}=\dfrac{12}{\overline{EF}-12}\\\sf6\overline{EF}-72=96\\\sf6\overline{EF}=72+96\\\sf\overline{EF}=\dfrac{168}{6}\\\sf\overline{EF}=28~cm$

$\sf\overline{DF}=12+\overline{EF}\\\sf\overline{DF}=12+28\\\huge\boxed{\boxed{\boxed{\boxed{\sf\overline{DF}=40~cm\checkmark}}}}$