HS║AE, L∈AE ⇒ HS║AL (1)
TA║SL, H∈TA ⇒ HA║SL (2)
Din (1)(2) ⇒ HALS - paralelogram ⇒ HA=LS, AL=SH
HS║AE ⇒ (Th. Thales) [tex] \frac{TH}{HA} = \frac{TS}{SE} [/tex]
[tex] \frac{3}{HA} = \frac{5}{8} =\ \textgreater \ HA = \frac{3*8}{5} = \frac{24}{5} = 4.8 dm [/tex] ⇒ HA = LS = 4.8 dm
TA║SL ⇒ [tex] \frac{ES}{ST} = \frac{EL}{LA} =\ \textgreater \ \frac{8}{5} = \frac{6}{LA} =\ \textgreater \ LA = \frac{6*5}{8} = \frac{3*5}{4} = \frac{15}{4} = 3.75 dm[/tex] ⇒ LA = SH = 3.75 dm
Perimetrul = 2*4.8 + 2*3.75 = 9.6 + 7.5 = 17.1 dm
Sper ca te-am ajutat! ^^
