Question

Problema din imagine, vă rog! Mulțumesc mult !

Answer 1

$\it Fie\ \ \Delta ABC-isoscel,\ AB=AC\ \ \ \ \ \ \ (1)\\ \\ \mathcal{P} =AB+AC+BC=28\ \stackrel{(1)}{\Longrightarrow} AB+AB+4=28|_{-4} \Rightarrow 2AB=24|_{:2} \Rightarrow \\ \\ \Rightarrow AB=12 \Rightarrow AC=12$

$\it Fie\ \ BCQM-trapez,\ MQ||BC,\ MQ=MB=QC=x,\ \ AM=AQ=12-x\\ \\ MQ||BC\ \stackrel{T.f.a.}{\Longrightarrow}\ \Delta AMQ\sim\Delta ABC \Rightarrow \dfrac{AM}{AB}=\dfrac{MQ}{BC} \Rightarrow \dfrac{12-x}{12}=\dfrac{x}{4} \Rightarrow \\ \\ \\ \Rightarrow 48-4x=12x|_{+4x} \Rightarrow 48=16x|_{:16} \Rightarrow x=3\ \Rightarrow MQ=BM=CQ=3cm$

$\it \mathcal{P}_{BCQM}=BC+CQ+QM+QB=4+3+3+3=13\ cm$