SOLUTION: A triangle ABC has a perimeter of 1.89m. AB + BC = 2AC. AB = 2BC.Find the length of the longest side.

Algebra ->  Trigonometry-basics -> SOLUTION: A triangle ABC has a perimeter of 1.89m. AB + BC = 2AC. AB = 2BC.Find the length of the longest side.      Log On


   

Question 1189233: A triangle ABC has a perimeter of 1.89m. AB + BC = 2AC. AB = 2BC.Find the length of the longest side.
Answer by greenestamps(13200) About Me  (Show Source):
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AB = 2BC

let BC = x
then AB = 2x

AB+BC = 2AC

2x+x = 2AC
3x = 2AC
AC = 1.5x

The perimeter is 1.89m:

2x+x+1.5x = 1.89
4.5x = 1.89
9x = 3.78
x = 3.78/9 = 0.42

The side lengths are
AB = 2x = 0.84m
BC = x = 0.42m
AC = 1.5x = 0.63m

ANSWER: The longest side is 0.84m