Răspuns:
Explicație pas cu pas:
a) ABCD dreptungi, AB=2·BC, P(ABCD)=36cm, ⇒2·(AB+BC)=36, ⇒AB+BC=18, ⇒2·BC+ BC=18, ⇒3·BC=18, ⇒BC=6cm, iar AB=2·6=12cm
Aria(ABCD)=AB·BC=12·6=72cm².
b) DG=6cm, AB║CD, ⇒ΔDGE~ΔBAE, ⇒DE/BE=GE/AE=DG/BA=6/12=1/2.
Deci, DE/BE=1/2=GE/AE. (1)
La fel, ΔCGF~ΔABF, ⇒CF/AF=GF/BF=CG/AB=6/12=1/2. Deci CF/AF=1/2=GF/BF. (2).
Din (1) și (2), ⇒GE/AE=CF/AF=1/2. Atunci, după Thales, ⇒EF║GC, deci EF║DC.
c) d(E,AD)=EH, unde EH⊥AD, deci EH║AB. Atunci ΔDEH~ΔDBA, ⇒EH/BA=DE/DB. Din
[tex]\dfrac{DE}{BE}=\dfrac{1}{2},~=>~\dfrac{DE}{BE+DE}=\dfrac{1}{2+1},~=>~\dfrac{DE}{DB}=\dfrac{1}{3},~[/tex]
Deci, EH/BA=1/3, ⇒EH/12=1/3, ⇒EH=(12·1)/3=4cm.
