Question

Um triângulo ABC tem lados AB,AC e BC que medem respectivamente 5cm 10cm e 9cm. Determine a medida da mediana relativa ao lado AC

Answer 1

$Sabendo\ que\ para\ Geometria\ Plana\ ,\ a\ f\acute{o}rmula\ para\ o\\ c\acute{a}lculo\ da\ mediana\ relativa\ a\ um\ lado\ \acute{e}\ expressa\ por\ :\\\\ \boxed{\boxed{M_A\ =\ \frac{1}{2} \ . \ \sqrt{\ 2\ .\ \Big(\ B^2\ +\ C^2\ \Big) \ - \ A^2}}}$

$Ent\tilde{a}o\ podemos\ reescrevendo\ a\ express\tilde{a}o\ acima\ :\\\\ M_{\overline{AC}}\ =\ \frac{1}{2}\ .\ \sqrt{\ 2\ .\ \Big(\ \overline{BC}^2\ +\ \overline{AB}^2 \ \Big) \ - \ \overline{AC}^2} \\\\ M_{\overline{AC}}\ =\ \frac{1}{2} \ . \ \sqrt{\ 2 \ . \ \Big( \ 9^2 \ + \ 5^2 \ \Big) \ - \ 10^2} \\\\ M_{\overline{AC}}\ =\ 2 \sqrt{7}$