SOLUTION: △ADE ~ △ABC. Given: DE = 3, AC = 32, EC = BC Find:BC

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Question 1193613: △ADE ~ △ABC.
Given: DE = 3, AC = 32, EC = BC
Find:BC
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

△ADE ~ △ABC.
triangles

Given: DE+=+3, AC+=+32, EC+=+BC
if triangles similar, corresponding sides are proportional

BC%2FDE=+AC%2FEA
EC%2FDE=AC%2FAE.....EC=32-AE and DE+=+3
%2832-AE%29%2F3=32%2FAE
AE%2832-AE%29=32%2A3
32AE-%28AE%29%5E2=96
%28AE%29%5E2-32AE%2B96=0
using quadratic formula we have
AE=%28-%28-32%29%2B-sqrt%28%28-32%29%5E2-4%281%29%2A9%29%29%2F%282%281%29%29
AE=31.71 or 0.28=>approximately

EC=32-AE=32-31.71=0.28
or
EC=32-AE=32-0.28=31.72

since EC%3EAE , use EC=31.72
then, since BC=EC
BC=31.72




Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The above solution is incorrect, because it is not given that either
△ADE or △ABC are right triangles, as she has assumed. 

However, there is not enough information given to solve your problem.
Both of the figures below show two correct solutions to the problem
using the given information.  You can check to be sure that all the
given information is correct.  Yet, in the first case, BC is 24, and
in the second case below, BC is 28.  There are an infinite number of
possible solutions.  You have obviously omitted something that was
given. 









Edwin