Question

trapezul abcd cu ab paralela cu cd ab =48 si cd=30 , iar diagonalelel ac =52 si bd=65 . stiind ca an interesctata cu bd = o ; calcula oa ob oc od

Answer 1

[tex]AB||CD\Longrightarrow \Delta AOB \sim \Delta COD\\\\ \frac{AO}{OC} = \frac{OB}{OD} = \frac{AB}{CD}\\\\ \frac{AO}{OC} = \frac{48}{30}= \frac{8}{5}\\\\ AO+ \frac{OC}{OC}=8+ \frac{5}{5} \\\\ \frac{AC}{OC}= \frac{13}{5} \Longrightarrow \frac{52}{OC}= \frac{13}{5}\Longrightarrow OC= \frac{52*5}{13}\Longrightarrow \bold{OC=20~cm} \\\\[/tex] 

[tex]\Longrightarrow AO=52-20 \Longrightarrow \bold{AO=32 ~cm} \\\\ \frac{OB}{OD} = \frac{48}{30}= \frac{8}{5}\\\\ OB+\frac{OD}{OD} =8+ \frac{5}{5}\\\\ \frac{BO}{OD}= \frac{13}{5}\\\\ \frac{65}{OD} = \frac{13}{5} \Longrightarrow OD= \frac{65*5}{13}\Longrightarrow \bold{OD=25~cm}\Longrightarrow OB=65-25\\\\\Longrightarrow \bold{OB=40~cm}[/tex]

Answer 2

Uite in Imaagine pentru prima diagonala pe a doua o faci singur ca esti baiet destept!!! Succes!!!