SOLUTION: △CDE ~ △CBA with ∠CDE ≅ ∠B. If CD = 10, CA = 18, and EB = 11, find CE.

Algebra ->  Formulas -> SOLUTION: △CDE ~ △CBA with ∠CDE ≅ ∠B. If CD = 10, CA = 18, and EB = 11, find CE.       Log On


   

Question 1193614: △CDE ~ △CBA with ∠CDE ≅ ∠B.
If CD = 10, CA = 18, and EB = 11, find CE.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
△CDE ~ △CBA with ∠CDE ≅ ∠B.
If CD+=+10, CA+=+18, and EB+=+11, find+CE.

similar triangles have proportional corresponding sides

CD%2FCB+=+CE%2FCA

Since CD+=+10 , CA+=+18 , CB+=+CE+%2B+EB , EB+=+11, then CB+=+CE+%2B+11 :

10%2F%28CE+%2B+11%29+=+CE%2F18

cross-multiplying:

+10+%2A18=CE%28CE+%2B+11%29

CE%5E2+%2B11CE+-+180+=+0
%28CE+%2B+20%29%28CE+-+9%29+=+0
CE+=+-20 or CE+=+9
disregard negative solution for the length
so, CE+=+9