If CE:EA:AD:DB=2:3:4:8, then what is [ACD]/[ABE]?
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?
Let angle A = 90º
CE = 2
EA = 3
AD = 4
DB = 8
[ACD]/[ABE] = 5/9
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
+876 
