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# If two sides of a triangle have lengths 2 and 5, which of th

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Joined: 14 Mar 2013
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GMAT Date: 12-03-2013
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If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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Updated on: 19 Nov 2013, 02:24
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Question Stats:

75% (00:32) correct 25% (00:29) wrong based on 464 sessions

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If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

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

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Originally posted by amgelcer on 19 Nov 2013, 02:20.
Last edited by Bunuel on 19 Nov 2013, 02:24, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 52231
Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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19 Nov 2013, 02:29
7
2
amgelcer wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

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

-----------------
+KUDOS is the way to say THANKS

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.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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19 Nov 2013, 02:28
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Sum of two sides should be greater than the third side.
Difference between two sides should be lesser tha the third side.

So, the third side lies in the range

3 < c < 7

So perimeter lies in the range

10 < p < 14

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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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03 Apr 2016, 15:38
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Here is my approach => the key here is to realise that x can have any value in the range => (3,7)
So none of the options are a MATCH => A
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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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27 Nov 2017, 11:19
amgelcer wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

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

We are given that two sides of a triangle have lengths 2 and 5, and we need to determine the possible perimeter of the triangle. Here we are being tested on the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, the sum of the lengths of the two shortest sides must be greater than the length of the longest side. Let’s evaluate the Roman numeral answer choices.

I. perimeter = 9

The two known sides sum to 7. If the perimeter is 9, then the 3rd side is 9 – 7 = 2, giving us sides of 2, 2, and 5. Since 2 + 2 = 4 is less than 5, 9 cannot be the perimeter of the triangle.

II. perimeter = 15

If the perimeter is 15, then the 3rd side is 15 – 7 = 8, giving us sides of 2, 5, and 8. Since 2 + 5 = 7 is less than 8, 15 cannot be the perimeter of the triangle.

III. perimeter = 19

If the perimeter is 19, then the 3rd side is 19 – 7 = 12 giving us sides of 2, 5, and 12. Since 2 + 5 = 7 is less than 12, 19 cannot be the perimeter of the triangle.

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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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10 Sep 2018, 17:13
Bunuel wrote:
amgelcer wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

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

-----------------
+KUDOS is the way to say THANKS

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.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Bunuel, what about the case when triangle is isosceles. Why Cann't we consider 2,2 and 5 as sides or 2,5,5 sides of triangle.

Thanks,
Amm
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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10 Sep 2018, 20:02
ammuseeru wrote:
Bunuel wrote:
amgelcer wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

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

-----------------
+KUDOS is the way to say THANKS

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.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Bunuel, what about the case when triangle is isosceles. Why Cann't we consider 2,2 and 5 as sides or 2,5,5 sides of triangle.

Thanks,
Amm

1. Sides of 2, 2, 5 won't create a triangle: 2 + 2 < 5.

2. The perimeter of {5, 5, 2} triangle is 12, which is in the range we got: 10 < {perimeter} < 14.
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Re: If two sides of a triangle have lengths 2 and 5, which of th &nbs [#permalink] 10 Sep 2018, 20:02
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# If two sides of a triangle have lengths 2 and 5, which of th

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