Kẻ NC//AB
Xét ΔMNC có AB//NC
nên MA/MN=MB/MC
=>MB/MC=3/4
=>MB=3/4MC
=>3/4MC=5/6MP
=>MC=5/6:3/4*MP=5/6*4/3*MP=10/9MP
=>\(S_{MNP}=\dfrac{9}{10}\cdot S_{MNC}\)
Vì AB//NC
nên ΔMAB đồng dạng với ΔMNC
=>\(\dfrac{S_{MAB}}{S_{MNC}}=\left(\dfrac{MA}{MN}\right)^2=\dfrac{9}{16}\)
=>\(S_{MAB}=\dfrac{9}{16}\cdot S_{MNC}\)
\(\dfrac{S_{MAB}}{S_{MNP}}=\dfrac{9}{16}:\dfrac{9}{10}=\dfrac{10}{16}=\dfrac{5}{8}\)
=>\(S_{MAB}=\dfrac{5}{8}\cdot S_{MNP}\)
=>\(\dfrac{S_{MAB}}{S_{ABPN}}=\dfrac{5}{3}\)
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