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+1
33
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avatar+47 

In trapezoid ABCD with bases AB and DC, diagonals intersect at point O. Find the length of diagonal BD, if BO=6 cm andAO/AC=3/4

 
 Jan 11, 2019
 #1
avatar+94296 
+1

Angle  AOB   =  Angle COD

Angle ABO = Angle CDO

So...by AA congruency....triangle AOB  is similar to triangle COD

 

Since  AO / AC = 3/4 ......then CO must be (1/3)AO  ⇒  3CO = AO

 

So

 

OD/ CO = OB / AO

 

OD / CO = 6/ (3CO)

 

OD / 1  = 6/3

 

OD = 2

 

So  BD =  BO + OD   =  6 + 2   =   8

 

 

 

cool cool cool

 
 Jan 11, 2019

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