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We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB is parallel to DE. If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

 Apr 20, 2022
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               A

                  

                         E

 

 B            D                C

 

If AB = AC  then the triangle is isosceles

 

If BC is 15   then AD  =   2 * 200 / 15    =     80/3

 

And because ABC is isosceles, then  DC = BD  = 15 /2

 

And since DE is parallel to AB  and AC is a transversal cutting both, then triangles   ABC  and EDC are similar because angle ACD = angle ECD   and angle BAC  = angle   DEC

 

And  since  BC = 2 DC.. then  2 is  the  scale factor between triagles ABC and EDC.....then the area of triangle  ABC  =  area of triangle EDC * scale factor ^2

 

So

 

200 =  area of EDC * 2^2

 

200 = area of EDC * 4

 

200  / 4  =  area of EDC  = 50

 

So  [ ABDE ]  =    area of ABC - area of EDC  =  200 -  50     =  150

 

 

cool cool cool

 Apr 21, 2022

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