vikasp99 wrote:

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

Dear

vikasp99,

I'm happy to respond.

This question tests one specific geometry fact: The Triangle Inequality. See:

Facts about Ordinary Triangles on the GMATThe

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

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)