Question

Perimetrul triunghiului ABC este de 48 cm. Determinati lungimile laturilor triunghiului, stiind ca (AB , AC ,BC) d.p (6,8,4)

Answer 1

$(AB,AC,BC)~ d.p.~ (6,8,4) \Rightarrow \dfrac{AB}{6}=\dfrac{AC}{8}=\dfrac{BC}{4}=k\Rightarrow AB=6k,\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~AC=8k\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~BC=4k.\\P_{ABC}=48 cm\\AB+BC+AC=48\\6k+4k+8k=48\\18k=48\\k=\dfrac{48}{18}=\dfrac{8}{3}\\AB=6k = 6\cdot \dfrac{8}{3}=16\ cm\\\\BC=4k= 4\cdot \dfrac{8}{3}=\dfrac{32}{3}\ cm\\\\AC=8k=8\cdot \dfrac{8}{3}=\dfrac{64}{3}\ cm$