Question 732184: A triangle has two sides that measure 4.56 cm and 8.65 cm. Which could be the measure of the third side?
A. 3.95 cm
B. 10.31 cm
C. 13.21 cm
D. 20.25 cm
Found 3 solutions by lynnlo, Alan3354, ikleyn:
Answer by lynnlo(4176)   (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A triangle has two sides that measure 4.56 cm and 8.65 cm. Which could be the measure of the third side?
A. 3.95 cm
B. 10.31 cm
C. 13.21 cm
D. 20.25 cm
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Only B, for the reasons given in a similar problem I did ~ 30 minutes ago.
Answer by ikleyn(53430)  (Show Source):
You can put this solution on YOUR website! .
A triangle has two sides that measure 4.56 cm and 8.65 cm. Which could be the measure of the third side?
A. 3.95 cm
B. 10.31 cm
C. 13.21 cm
D. 20.25 cm
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This is a good problem on triangles, but it has a TRAP,
so it requires an accuracy.
According to the triangle inequalities,
- the third side of a triangle is always shorter than the sum of two other sides,
- and the third side of a triangle is always longer than the difference of two other sides.
In this given problem, the sum of the measures of two given sides is 4.56 + 8.65 = 13.21 cm.
THEREFORE, third side can not be (C) or (D).
In this given problem, the difference of the measures of two given sides is 8.65 - 4.56 = 4.09 cm.
THEREFORE, third side can not be (A).
By exclusion, of four given options, only (B) satisfies the condition.
So, the correct answer is (B).
Solved, with explanations.
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The answer in the post by @lynnlo is incorrect.
So, simply ignore his post.
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