Question

in triunghiul ABC ,AM-mediana , M apartine (BC), iar MN - inaltime in AMC , N apartine (AC) .Stiind ca AC=28 cm si MN=2,5 dm , calculati aria ABC

Answer 1

   
[tex]\displaystyle\\ \text{In triunghiul AMC cunoastem Baza AC si inaltimea MN.}\\\\ A_{\Delta AMC}=\frac{AC\times MN}{2}=\frac{28 \times25}{2}=\frac{700}{2}= \boxed{350~cm^2}\\\\ \text{Mediana imparte orice fel de triunghi in 2 triunghiuri echivalente.}\\ \text{Triunghiurile echivalente sunt triunghiuri care au aceeasi arie.}\\\\\Longrightarrow~~A_{\Delta AMB}=A_{\Delta AMC}=\boxed{350~cm^2}\\\\ \Longrightarrow~~A_{\Delta ABC}=A_{\Delta AMB}+A_{\Delta AMC}=350+ 350=\boxed{\boxed{700~cm^2}} [/tex]