ABC is a triangle whose sides AB and BC have length of 3 and 5 respect

Question

ABC is a triangle whose sides AB and BC have length of 3 and 5 respectively. Which of the following could be the length of side AC?

(I) 8 
(II) 12 
(III) 0.5

A) (I) only 
B) (II) only 
C) (III) only 
D) (I) and (II) only 
E) None

mikemcgarry · Answer

Dear vikasp99 , I'm happy to respond. :-)

This question tests one specific geometry fact: The Triangle Inequality. See: Facts about Ordinary Triangles on the GMAT The Triangle Inequality says that the sum of any two sides a triangle must be greater than the third. Let x be the third side. If it's the longest side, it must be true that x < 3 + 5 x < 8 So it must be true that x is less than 8. (II) is definitely out, and (I) is out also. Think about it: if the third side were 8, the sides of 3 and 5 would have to lie flat, stretched their full length, just to connect to the two ends of the 8, and then we would have line segments on top of one another, rather than a triangle. A triangle has to have an inside with area. Suppose x is the smallest side; then 5 would be the largest side, and it would be true that x + 3 > 5 x > 2 Combine these: 2 < x < 8. That's the range of possible lengths of the third sides, and none of the three numbers given are in this range. OA = (E) Does all this make sense? Mike :-)

gvvsnraju@1 · Answer

None of the given lengths are correct since any two lengths of given triangle must be greater than Third Side. Regards Narayana Raju

MHIKER · Answer

The property of tringle is here;
The Sum of two sides must be larger than the third side.

(I) 8; can't be. Because 3+5 = 8 is equal to 8 not larger. 
(II) 12; can't be, because the sum of the other two sides is lesser than 12.
(III) 0.5 can't be, because if it is added with any other side the sum can't the greater third one.

so the answer is none. E.

Abhishek009 · Answer

1. The difference of two sides must be less than the third side - 2
2. The sum of two sides must be larger than the third side - 8

2 < Third Side < 8

Hence, None of the given options follows , answer must be (E)

ABC is a triangle whose sides AB and BC have length of 3 and 5 respect

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ABC is a triangle whose sides AB and BC have length of 3 and 5 respect

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