SOLUTION: GIVEN: In ABC, DE // BC, AD = 9, AE = 12, DE = 10,DB = 18. Find, BC, CE, and AC.

Algebra ->  Triangles -> SOLUTION: GIVEN: In ABC, DE // BC, AD = 9, AE = 12, DE = 10,DB = 18. Find, BC, CE, and AC.       Log On


   

Question 1205859: GIVEN: In ABC, DE // BC,
AD = 9, AE = 12,
DE = 10,DB = 18.
Find,
BC, CE, and AC.
Answer by MathLover1(20850) About Me  (Show Source):
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GIVEN:
AD+=+9
+AE+=+12
DE+=+10
DB+=+18
triangle ABC is similar to triangle DEA, and similar triangles have proportional corresponding side lengths
AB=AD%2BBD+=+9%2B18=27
AC=12%2By
then
AD%2FAB=10%2Fx
9%2F27=10%2Fx
9x=270
x=30

and
AD%2FAB=12%2F%2812%2By%29
9%2F27=12%2F%2812%2By%29
9%2812%2By%29=12%2A27
9%2812%2By%29=%2812%2A27%29%2F9
12%2By=12%2A3
12%2By=36
y=36-12
y=24
answer:
BC=30
CE=24
AC=12%2B24=36