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Najlepsze rozwiązanie

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  rzbyszek 26.3.2011 (07:03)

  \left\{\begin{array}{l} a \cdot b=20 \\ b \cdot c=24 \\ a \cdot c=30 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ \frac{20}{b} \cdot c=30 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ \frac{20}{ \frac{24}{c}} \cdot c=30 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ 20 \cdot \frac{c}{24}=30 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ c^2=30 \cdot \frac{6}{5} \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ c^2=36 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{c} \\ c=6 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = \frac{24}{6} \\ c=6 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{b} \\ b = 4 \\ c=6 \end{array}
  
  \left\{\begin{array}{l} a= \frac{20}{4} \\ b = 4 \\ c=6 \end{array}
  
  \left\{\begin{array}{l} a=5 \\ b = 4 \\ c=6 \end{array}
  
  V=a \cdot b \cdot c=4 \cdot 5 \cdot 6=120cm^3
  
  Odp.: Objętość prostopadłościanu wynosi 120cm^3

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