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We know line DE is parallel to line BC. Given the Area of ADE=9 and Area of CDE=6 , find the Area of ABC.



 

 Oct 22, 2018
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Triangles  ADE  and DCE  are under the same height....so....their areas are to each other as their bases.....so  AD /DC  =  9 / 6  =  3 / 2

 

So...AD   /  AC  =   3 / 5

 

And triangles ADE  and ABC are similar

 

So......the scale factor of  AC / AD  =  5/3

 

And the area of triangle ABC  =  [scale factor AC /AD]^2  *  area of triangle ADE =

 

(5/3)^2  *  9  =

 

 ( 25 / 9 )  *  9  =

 

25  =  [ ABC ]

 

 

cool cool cool

 Oct 22, 2018

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