Geometry

[VenugopalGurram]

k is a Positive integer and 2<k<7.
What is the Value of k if 2,k and 7 are the sides of the triangle.

A)3
B)4
C)5
D)6
E)7

[Jim@StratusPrep]

Has to be 6.

The sum of any two sides must be greater than the other side.

[sana.noor]

it could be 5 also because 5 is less than 7 and greater than 2...

[Brent@GMATPrepNow]

k is a Positive integer and 2<k<7.
What is the Value of k if 2,k and 7 are the sides of the triangle.

A)3
B)4
C)5
D)6
E)7

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
|A-B| < third side < A+B

In this question, the two given sides have length 2 and 7.
So, |2-7| < third side < 2+7
Or 5 < third side < 9
So the third side can have any length between 5 and 9.
Of course, we're also told that k < 7. So, among the answer choices, only 6 works.
Answer: D

Cheers,
Brent

[jermy]

According to the triangle inequality rule sum of two sides is greater than third side and difference of two sides in less than third side, so
2 +7 >k and 7-2<k
9>k>5
therefore k is either 6 or 7
but given that k<7
hence k will be 6