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OG11, PS# 45. Someone please clarify.

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by GMAT Sux » Wed Aug 13, 2008 3:33 pm
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

I understand that in a triangle, the length of the longest side must be smaller than the sum of the lengths of the two other sides.

I thought the answer would be C but it's A. My thinking was that the two sides given 3+8=11. So wouldn't 5 and 8 fit since they're smaller than 11?

Someone please clarify this, thanks.
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by parallel_chase » Wed Aug 13, 2008 3:51 pm
Let a, b & c are three sides of the triangle

Rule:

a+b > c
a+c > b
b+c > a

c-a > b
c-b > a
b-a > c


Now insert the values

Let a=3 and b=8

8-3 = 5

8+3= 11

Therefore c cannot be equal to 5 or 11. Hence 8 is the answer.
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by sumithshah » Thu Aug 14, 2008 11:19 am
An easier way to remember the rule mentioned above

If A and B are two sides of a triangle the third side, C is given by

A-B<C<A+B


Hope this helps
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