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ABCD is a trapezoid, and AB is parallel to CE.  If BD = 8 and DE = 7, then find the ratio of the area of triangle ADB to the area of triangle CDE.

 

 Dec 16, 2020
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Since ADCB is a trapezoid, then AD is also parallel to BC

And note that angle  EBC   = angle BDA

And because AB is parallel to CE, then angle BEC  = angle DBA

 

So  triangle  BEC  is similar to triangle  DBA

 

So    BE  and  DB   are corresponding sides

 

And the ratio of the area of DBA to DEC  = (BD/ BE)^2 =  (8/15)^2  = 64/225

 

And   triangles EDC  and BEC  share  equal altitudes  so  their areas are to each other  as  their bases

 

ED = 7      BE  = 15

 

So    area   EDC =  (7/15)area  of triangle BEC  ⇒  EDC/ BEC =  7/15 =  105/ 225

 

And the ratio of the area of DBA to BEC  =  (8/15)^2  =  64/225   ⇒  DBA / BEC = 64/225

 

So

 

(DBA / BEC)         64 / 225             [ DBA ]           64

__________  =    ________  =      ______  =    ____

(CDE /  BEC)        105 / 225           [ CDE  ]        105

 

 

 

cool cool cool

 Dec 16, 2020

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