SOLUTION: In triangle ABC,D and E are points on the sides AB and AC respectively such that DE parallel to BC. If AD:DB =3/4 and AC =15 cm, find AE.

Algebra ->  Formulas -> SOLUTION: In triangle ABC,D and E are points on the sides AB and AC respectively such that DE parallel to BC. If AD:DB =3/4 and AC =15 cm, find AE.      Log On


   



Question 1181299: In triangle ABC,D and E are points on the sides AB and AC respectively such that DE parallel to BC. If AD:DB =3/4 and AC =15 cm, find AE.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If AD%2FDB+=3%2F4 and DE || BC
by proportionality theorem, we have
AD%2FDB=AE%2FEC ........... substitute AD%2FDB+=3%2F4, and add 1 to both sides we have
3%2F4%2B1=AE%2FEC%2B1
7%2F4=%28AE%2BEC%29%2FEC+
7%2F4=AC%2FEC ........substitute+AC+=15
7%2F4=15%2FEC........cross multiply
7EC=15%2A4
7EC=60
EC=60%2F7
EC=8.6

now find AE
AC=AE%2BEC
15=AE%2B8.6
15-8.6=AE
AE=6.4