Question

Un tablou avangardist cu peisaj de iarna are forma unui trapez ABCD, AB||DC, AB=12 dm, CD=36dm. Daca AC se intersecteaza cu BD={O} si AC=20dm, BD= 28dm, calculati lunimile segmentelor [AO], [OB], [OC], [OD].

Answer 1

ABCD-trapez⇒ AB||CD⇒ ΔAOB asemenea ΔCOD⇒
AO/OC=BO/OD=AB/CD=12/36=1/3
AO/OC=1/3⇒ OC=3AO⇒ OC+OA=20⇒3AO+AO=20⇒4AO=20⇒AO=20:4⇒
AO=5 cm⇒ OC=20-5=15 cm

BO/OD=1/3⇒ OD=3OB⇒ OB+OD=28⇒ 3OB+OB=28⇒ 4OB=28⇒ OB=28:4
⇒OB=7 cm⇒ OD=28-7=21 cm