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If CE:EA:AD:DB=2:3:4:8, then what is [ACD]/[ABE]?

 

 Jul 1, 2021
 #1
avatar+795 
+1

Hint: WLOG, define side lengths for the triangles given ratios.

 

Hint 2: Construct a line from C to B.

 

Hint 3: Define values for those areas.

 

I have done all of these, but I only have 3 equations but 4 variables. Any thoughts?

edited by MathProblemSolver101  Jul 1, 2021
edited by MathProblemSolver101  Jul 1, 2021
 #2
avatar+1569 
+5

Let angle A = 90º

CE = 2

EA = 3

AD = 4

DB = 8

[ACD]/[ABE] = 5/9

 Jul 1, 2021
edited by civonamzuk  Jul 1, 2021
 #3
avatar+121047 
+3

Let   the  height  of  triangle ACD =  H      and  the base =  B

 

Then   the    height of   triangle   ABE  = 3/(3 + 2) * H  =  (3/5) H   and  the  base =  (8+ 4) / 4  * B =   (3)B

 

So

 

  [ ACD ]   /  [ ABE ]  =

 

[ BH  ]  /   [ (3B  * (3/5) H  ]  =

 

BH  /  (9/5) BH )  =

 

1 / (9/5)  =

 

5/9

 

 

cool cool cool

 Jul 1, 2021
edited by CPhill  Jul 1, 2021
edited by CPhill  Jul 1, 2021

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