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Believe ans is A as k can be 3,4,5 or 6. for all cases except k=6, sum of teo sides can be less than equal to third side which should not be true

As as per triangle property sum of two sides is greater than third side. _________________

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Re: If k is an integer and 2 < k < 7, for how many different [#permalink]

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13 Jul 2012, 02:59

Expert's post

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SOLUTION

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one (B) two (C) three (D) four (E) five

Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

According to the above the following must be true: \((7-2)<k<(7+2)\) --> \(5<k<9\). So, \(k\) could be 6, 7 or 8. Since also given that \(2 < k < 7\), then \(k=6\). Hence \(k\) can take only one value: 6.

Re: If k is an integer and 2 < k < 7, for how many different [#permalink]

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20 May 2014, 04:17

Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Above relationship is in the core of this solution. Many times I have found students having difficulty is assimilating this concept.

Best way to get this concept is trying to actually draw triangles which contradict this. For example, try to draw a triangle with following sides (actual scale)

4, 3, 8

Once you failed, you will realize that The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. _________________

Re: If k is an integer and 2 < k < 7, for how many different [#permalink]

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09 Aug 2015, 14:35

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