Đáp án:
$d(B;(SCD)) = \dfrac{3a\sqrt{34}}{17}$
Giải thích các bước giải:
Ta có:
$AD = 2BC$
$\Rightarrow S_{ABD} = 2S_{BCD}$
$\Rightarrow S_{BCD} = \dfrac13S_{ABCD}$
$\Rightarrow V_{S.BCD} = \dfrac13V_{S.ABCD} = \dfrac13\cdot 6a^3$
$\Rightarrow V_{S.BCD} = 2a^3$
Ta lại có:
$\quad V_{S.BCD} = V_{B.SCD} = 2a^3$
$\Leftrightarrow \dfrac13S_{SCD}.d(B;(SCD)) = 2a^3$
$\Leftrightarrow\dfrac13\cdot a^2\sqrt{34}\cdot d(B;(SCD)) = 2a^3$
$\Leftrightarrow d(B;(SCD)) = \dfrac{3a\sqrt{34}}{17}$
