Question 854546: The question I have for a work sheet says "the measures of the triangle are 3:4:5. Find the lengths if the perimeter is 85cm".
Found 2 solutions by richwmiller, DrBeeee:
Answer by richwmiller(17219)   (Show Source):
Answer by DrBeeee(684)  (Show Source):
You can put this solution on YOUR website! This is a job for the Nicole "n". So named after one of my super math students.
Given the ratio of the sides of a triangle as
(1) 3:4:5
Nicole says that the actual lengths are given by
(2) 3n:4n:5n which does not effect the ratios.
The perimeter, p, is the SUM of the sides or
(3) p = 3n + 4n + 5n or
(4) p = 12n
You're given that the perimeter is 85, so we have
(5) 12n = 85 or
(6) n = 85/12, not a pretty number, but at least rational.
The "real" sides are
(7) 3*85/12:4*85/12,5*85/12 or
(8) 255/12:340/12:425/12
Let's check Nicole using (3).
Is (255/12 + 340/12 + 425/12 = 85)?
Is (1020/12 = 85)?
Is (85 = 85)? Yes
Answer: The lengths of the triangle's sides are 255/12, 340/12 and 425/12.
PS some of the sides' fractions simplify, but I left them as is to give us the benefit of visualizing the ratio. If your teacher want the simplist form use 85/4, 85/3, 425/12.
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