SOLUTION: An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to t

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Question 1022222: An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
A) 18.8 cm
B) 24.2 cm
C) 42.0 cm
D) 72.7 cm
Found 2 solutions by FrankM, MathTherapy:
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
The longest side, 2X must be less than the sum of the 2 shorter sides, X+21

2X%3CX%2B21

X%3C21

2X%3C42

C

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
A) 18.8 cm
B) 24.2 cm
C) 42.0 cm
D) 72.7 cm
Since 21 is one of the shorter sides, it follows that 2x MUST be the longest side

We then get: 2x < x + 21 

2x - x < 21

x < 21

Therefore, the longest side, or 2x < 42 

Since the longest side, or 2x < 42, then the longest side's length can either be 18.8 cm (choice A), or 24.2 cm (choice B),

but since one of the shorter sides is 21, the