Vì MN//PQ nên \(\frac{MN}{BC}=\frac{AM}{AB}\Rightarrow MN=\frac{AM}{AB}.a\left(1\right)\)
Lại có MP//AH nên: \(\frac{MP}{AH}=\frac{BM}{AB}\)
\(\Leftrightarrow1-\frac{MP}{AH}=1-\frac{BM}{AB}\)
\(\Leftrightarrow1-\frac{MP}{AH}=\frac{AB-BM}{AB}\)
\(\Leftrightarrow1-\frac{MP}{AH}=\frac{AM}{AB}\)
\(\Leftrightarrow\frac{MN}{h}=1-\frac{AM}{AB}\)( vì MN=MP, ABCD là h/vuông)
\(\Leftrightarrow MN=h-\frac{h.AM}{AB}\left(2\right)\)
Vì (1)=(2) nên \(\frac{AM}{AB}.a=h-\frac{h.AM}{AB}\)
\(\frac{\Leftrightarrow\left(a+h\right)AM}{AB}=h\)
\(\Leftrightarrow\frac{AM}{AB}=\frac{h}{a+h}\)
Có MN//BC nên \(\frac{AM}{AB}=\frac{MN}{a}=\frac{h}{a+h}\)
\(\Rightarrow MN=\frac{ah}{a+h}\)
