Question

Daca un tiriunghi ABC~MNP, AB=9 cm si AC=12 cm iar raportul de asemanare este de 3/7 calculati lungimile segmentelor MN si Mp

Answer 1

AB/MN=BC/NP=AC/MP=3/7
9/MN=3/7 =>MN=(9×7)/3=21 cm
12/MP=3/7 =>MP=(12×7)/3=28 cm

Answer 2

$\it \Delta ABC\sim\Delta MNP \Rightarrow \dfrac{AB}{MN}=\dfrac{AC}{MP} =k\ \ \ \ (1)\\ \\ \\ k = \dfrac{3}{7}\ \ \ \ (2)\\ \\ \\ (1),(2) \Rightarrow \begin{cases}\it\dfrac{9}{MN}=\dfrac{3}{7} \Rightarrow MN=\dfrac{9\cdot7}{3}=3\cdot7=21\ cm\\ \\ \it\dfrac{12}{MP}=\dfrac{3}{7} \Rightarrow MP=\dfrac{12\cdot7}{3}=4\cdot7=28\ cm \end{cases}$