Răspuns:
Explicație pas cu pas:
AB=12, CD=20, AD=8, BC=12.
ΔDEC≅ΔAEB, deci
[tex]\frac{DC}{AB}=\frac{DE}{AE} =\frac{CE}{BE}.~Inlocuim,~\frac{20}{12}=\frac{DA+AE }{AE}=\frac{CB+BE}{BE},~deci~\frac{5}{3}=\frac{DA}{AE}+1=\frac{CB}{BE}+1,~deci\\\frac{5}{3}=\frac{8}{AE}+1=\frac{12}{BE}+1,~deci~\frac{5}{3}=\frac{8}{AE}+1,~\frac{5}{3}-1=\frac{8}{AE},~\frac{2}{3}= \frac{8}{AE},~deci,~AE=\frac{3*8}{2}=12.\\Din~\frac{5}{3}=\frac{12}{BE}+1,~\frac{5}{3}-1= \frac{12}{BE},~\frac{2}{3} =\frac{12}{BE}.~deci~BE=\frac{3*12}{2}=18cm.\\[/tex]
Atunci P(ΔEAB)=AE+EB+AB=12+18+12=42cm.
