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We know $\overline {DE}\parallel \overline {BC}.$ Given $[ADE]=9$ and $[CDE]=6,$ find $[ABC].$

https://latex.artofproblemsolving.com/6/4/2/6426d0d7650c668b5b900bdc52c9030f0880d2bb.png

 Oct 15, 2019
 #1
avatar+104911 
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[ ADE]  and [ CDE]  are on the same base, ED

 

Therefore..since [CDE]  = 6  and [ADE]  = 9 ...the height of  [CDE]  must be (6/9) = (2/3) the height of [ ADE]

 

Therfore  the height of [ABC]   =  height of ADE + (2/3)height of ADE   =  (5/3) ADE

 

And since DE is parallel to AB  then    [AED] and [ ABC]   are similar

 

So...  [ ABC]  =  (5/3)^2 * area of [ AED]  =  (25/9)(9)  =  25

 

 

 

cool cool cool

 Oct 15, 2019
edited by CPhill  Oct 15, 2019
edited by CPhill  Oct 15, 2019
edited by CPhill  Oct 15, 2019

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