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If p is the perimeter of a triangle with one side of 7 and a

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sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

If p is the perimeter of a triangle with one side of 7 and a [#permalink]

20 Sep 2018, 16:47

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If p is the perimeter of a triangle with one side of 7 and another side of 9, what is the range of possible values for p?
(A) 2 < p < 16
(B) 3 < p < 17
(C) 18 < p < 32
(D) 18 < p < 33
(E) 17 < p < 63

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shivankkhanna

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Joined: 07 Sep 2018

Posts: 29

Re: If p is the perimeter of a triangle with one side of 7 and a [#permalink]

20 Sep 2018, 21:45

explain pls.

sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Re: If p is the perimeter of a triangle with one side of 7 and a [#permalink]

24 Sep 2018, 08:34

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Explanation

From the Third Side Rule, any side of a triangle must be greater than the difference of the other two sides and less than their sum. Since 9 – 7 = 2 and 9 + 7 = 16, the unknown third side must be between 2 and 16, not inclusive.

To get the lower boundary for the perimeter, add the lower boundary of the third side to the other two sides: 2 + 7 + 9 = 18. To get the upper boundary for the perimeter, add the upper boundary for the third side to the other two sides: 16 + 7 + 9 = 32. Thus, p must be between 18 and 32, not inclusive—in other words, 18 < p < 32.
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Re: If p is the perimeter of a triangle with one side of 7 and a [#permalink]

10 May 2022, 08:32

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