a: Vì ABCD là hình thang có \(AB=\dfrac{1}{3}CD\)

nên \(S_{BAD}=\dfrac{1}{3}\cdot S_{BDC}\)

Vì BD=2DE

nên \(BD=\dfrac{2}{3}BE\)

=>\(S_{BAD}=\dfrac{2}{3}\cdot S_{ABE}\)

=>\(S_{ABE}=\dfrac{3}{2}\cdot S_{BAD}\)

Vì DB=2DE

nên \(S_{CBD}=2\cdot S_{CDE}\)

=>\(S_{CDE}=\dfrac{1}{2}\cdot S_{CBD}=\dfrac{1}{2}\cdot3\cdot S_{BAD}=\dfrac{3}{2}\cdot S_{BAD}\)

=>\(S_{ABE}=S_{CDE}\)

a: Ta có: AK=KO=OH

=>\(AK=KO=OH=\dfrac{1}{3}AH\)

=>\(AO=\dfrac{2}{3}AH;AK=\dfrac{1}{3}AH\)

Xét ΔAHB có EK//BH

nên \(\dfrac{AE}{AB}=\dfrac{AK}{AH}\)

=>\(\dfrac{AE}{AB}=\dfrac{1}{3}\)

Xét ΔABH có MO//BH

nên \(\dfrac{AM}{AB}=\dfrac{AO}{AH}\)

=>\(\dfrac{AM}{AB}=\dfrac{2}{3}\)

Xét ΔABC có EF//BC

nên \(\dfrac{EF}{BC}=\dfrac{AE}{AB}\)

=>\(\dfrac{EF}{BC}=\dfrac{1}{3}\)

=>\(EF=\dfrac{BC}{3}=\dfrac{30}{3}=10\left(cm\right)\)

Xét ΔABC có MP//BC

nên \(\dfrac{MP}{BC}=\dfrac{AM}{AB}\)

=>\(\dfrac{MP}{30}=\dfrac{2}{3}\)

=>\(MP=20\left(cm\right)\)

b: Xét ΔAMP và ΔABC có 

\(\widehat{AMP}=\widehat{ABC}\)(hai góc đồng vị, MP//BC)

\(\widehat{MAP}\) chung

Do đó: ΔAMP~ΔABC

=>\(\dfrac{S_{AMP}}{S_{ABC}}=\left(\dfrac{AM}{AB}\right)^2\)

=>\(\dfrac{S_{AMP}}{10.8}=\dfrac{4}{9}\)

=>\(S_{AMP}=4,8\left(dm^2\right)\)

Xét ΔAEF và ΔABC có

\(\widehat{AEF}=\widehat{ABC}\)(hai góc đồng vị, EF//BC)

\(\widehat{FAE}\) chung

Do đó: ΔAEF~ΔABC

=>\(\dfrac{S_{AEF}}{S_{ABC}}=\left(\dfrac{AE}{AB}\right)^2=\dfrac{1}{9}\)

=>\(S_{AEF}=\dfrac{10.8}{9}=1,2\left(dm^2\right)\)

Ta có: \(S_{AEF}+S_{MEFP}=S_{AMP}\)

=>\(S_{MEFP}+1,2=4,8\)

=>\(S_{MEFP}=3,6\left(dm^2\right)\)

Đức đã đi đc số phần quãng đường là
1/7+6/21+3/12=19/28(quãng đường)
=>Đức đã đi đc 19/28 quãng đường

\(\dfrac{3}{4}\) x X + \(\dfrac{3}{10}\) = \(\dfrac{7}{25}\)

\(\dfrac{3}{4}\) x X          = \(\dfrac{7}{25}-\dfrac{3}{10}\)

\(\dfrac{3}{4}\) x \(X\)         = \(\dfrac{-1}{50}\)

       X          = \(\dfrac{-1}{50}\):\(\dfrac{3}{4}\)

       X          = \(\dfrac{-4}{150}\)

3/4 x X + 3/10 = 7/25

3/4 x X =7/25-3/10

3/4 x X=-1/50

X=-1/50:3/4

X=-7/25

cho xin 5 sao đi

@Chu Khánh Minh Châu: m làm như là m giỏi lắm í

105

3570 : 34 = 105