Đáp án: $MN=16$
Giải thích các bước giải:
Gọi $AC\cap MN=E$
Ta có $DM=2AM$
$\to \dfrac{AM}{DM}=\dfrac12$
$\to \dfrac{AM}{DM+AM}=\dfrac1{1+2}$
$\to \dfrac{AM}{AD}=\dfrac{1}{3}$
Mà $MN//CD\to ME//CD\to \dfrac{AE}{AC}=\dfrac{ME}{CD}=\dfrac{AM}{AD}=\dfrac13$
$\to ME=\dfrac13CD=8$
Ta có:
$\dfrac{AE}{AC}=\dfrac13\to 1-\dfrac{AE}{AC}=1-\dfrac13\to \dfrac{CE}{CA}=\dfrac23$
Lại có $MN//AB\to NE//AB$
$\to \dfrac{NE}{AB}=\dfrac{CE}{CA}=\dfrac23$
$\to NE=\dfrac23AB=8$
$\to MN=ME+NE=16$