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

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

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New post Updated on: 19 Nov 2013, 03:24
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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, 03:20.
Last edited by Bunuel on 19 Nov 2013, 03:24, edited 1 time in total.
Edited the question.
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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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New post 19 Nov 2013, 03:29
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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.

Answer: 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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New post 19 Nov 2013, 03:28
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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

Answer is 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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New post 03 Apr 2016, 16:38
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Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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New post 27 Nov 2017, 12:19
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.

Answer: 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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New post 10 Sep 2018, 18:13
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.

Answer: A.


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
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Joined: 02 Sep 2009
Posts: 50007
Re: If two sides of a triangle have lengths 2 and 5, which of th  [#permalink]

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New post 10 Sep 2018, 21:02
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.

Answer: A.


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If two sides of a triangle have lengths 2 and 5, which of th &nbs [#permalink] 10 Sep 2018, 21:02
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