Question

trapezul ABCD are bazele AB||CD, AB=72cm,, CD= 32cm, diagonala AC=65cm si BD=78cm , stiind ca AC si BD ={0} .Calculați lungimea OA,OB,OC,OD​

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{OA}{OC} =\frac{OB}{OD} =\frac{72}{32} \\\frac{OA}{OC} =\frac{OB}{OD} =\frac{9}{4}$

$\frac{OA}{OC} =\frac{9}{4}$

$\frac{OA+OC}{OC} =\frac{9+4}{4}$

$\frac{CA}{OC} =\frac{13}{4}$

$\frac{65}{OC} =\frac{13}{4}$

OC=20 ⇒ OA=65-20=45

$\frac{OB}{OD} =\frac{9}{4}$

$\frac{OB+OD}{OD} =\frac{9+4}{4}$

$\frac{BD}{OD} =\frac{13}{4}$

$\frac{78}{OD} =\frac{13}{4}$

OD=24 ⇒OB=78-24=54