Posted by james on .
B is the midpoint of AC, D is the midpoint of CE, and Bd=14. find AE.
B is the midpoint of AC, D is the midpoint of CE and BD=7. Find AE.

geometry 
Steve,
Just lay out the points on the line
BD contains the right half of BC and the left half of CE
So, what's left is the same length: The left half of AC and the right half of CE
AE = AB + BC + CD + DE
but BD = BC + CD = 14
so,
AE = AB + 14 + DE
However,
AB = BC and CD = DE so AB+DE = BC+CD = 14
AE = 14 + 14 = 28
With that in hand, the 2nd problem should be trivial.