SOLUTION: help me solve this show the work too. in triangle ABC, line ED connects the midpoint of line AB and AC. The length of linE ED is 2x+3 and the length of line BC is 7x-3. Find the

Algebra ->  Triangles -> SOLUTION: help me solve this show the work too. in triangle ABC, line ED connects the midpoint of line AB and AC. The length of linE ED is 2x+3 and the length of line BC is 7x-3. Find the      Log On


   

Question 395122: help me solve this show the work too.
in triangle ABC, line ED connects the midpoint of line AB and AC. The length of linE ED is 2x+3 and the length of line BC is 7x-3. Find the value of x ED and BC.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
By connecting the midpoints of AB and AC, you have forme two similar triangles, ABC and AED. Using the fact that in similar triangles, corresponding sides are proportional, we can write:
ED%2FBC+=+AD%2FAC
Substituting: ED+=+2x%2B3 and BC+=+7x-3 we get:
%282x%2B3%29%2F%287x-3%29+=+AD%2FAC But, because D is the midpoint of AC, AD+=+%281%2F2%29AC, so...
%282x%2B3%29%2F%287x-3%29+=+1%2F2 Cross-multiplying, we get...
4x%2B6+=+7x-3 Solve for x:
6+=+3x-3
3x+=+9
x+=+3 so...
ED+=+2x%2B3 Substitute x=3.
ED+=+9 and...
BC+=+7x-3
BC+=+18