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BN = 2/5 × BC
BC = 5/2 × BN
Diện tích ∆ABC:
9,6 × 5/2 = 24 (cm²)
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BM+MC=BC
=>\(MC=BC-BM=BC-\dfrac{1}{3}BC=\dfrac{2}{3}BC\)
MC=2/3BC
=>\(S_{AMC}=\dfrac{2}{3}\cdot S_{ABC}\)
=>\(60=\dfrac{2}{3}\cdot S_{ABC}\)
=>\(S_{ABC}=60:\dfrac{2}{3}=90\left(cm^2\right)\)
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\(1,\\ a,=\dfrac{7}{19}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)=\dfrac{7}{19}\times1=\dfrac{7}{19}\\ b,=\dfrac{2}{5}+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)=\dfrac{2}{5}+1=\dfrac{7}{5}\\ 2,\\ a,=15\times\left(\dfrac{2121}{4343}+\dfrac{222222}{434343}\right)\\ =15\times\left(\dfrac{2121:101}{4343:101}+\dfrac{222222:10101}{434343:10101}\right)\\ =15\times\left(\dfrac{21}{43}+\dfrac{22}{43}\right)=15\times\dfrac{43}{43}=15\times1=15\)
\(3,\)
Cạnh \(AC=\) chu vi ABC \(-AB-BC=\dfrac{4}{5}-\dfrac{1}{5}-\dfrac{1}{4}=\dfrac{3}{5}-\dfrac{1}{4}=\dfrac{7}{20}\left(m\right)\)
Vì \(\dfrac{7}{20}>\dfrac{5}{20}>\dfrac{4}{20}\Rightarrow\dfrac{7}{20}>\dfrac{1}{4}>\dfrac{1}{5}\) nên \(AC>BC>AB\)
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