Question

3 In triungiul ABC consideram punctul D interior laturii AB si constrium DE || BC, E apartine AC stiind ca:
a) AD=4cm, DE=8cm, EA=1-cm si AB=14cm , calculati Pabc

Answer 1

$\it DE||BC\ \stackrel{T.f.a.}{\Longrightarrow}\ \Delta ABC\sim\Delta ADE\ \Rightarrow\ k=\dfrac{AB}{AD}=\dfrac{14^{(2}}{4}=\dfrac{7}{2}=3,5$

Raportul perimetrelor celor două triunghiuri este egal cu raportul

de asemănare, k.

$\it \dfrac{\mathcal{P}_{ABC}}{\mathcal{P}_{ADE}}=k \Rightarrow\ \dfrac{\mathcal{P}_{ABC}}{4+8+1}=3,5\Rightarrow\dfrac{\mathcal{P}_{ABC}}{13}=3,5\ \Rightarrow \mathcal{P}_{ABC}=13\cdot3,5=45,5$