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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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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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[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Nov 2013, 02:24, edited 1 time in total.
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Re: If two sides of a triangle have lengths 2 and 5, which of th [#permalink]

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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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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

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+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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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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New post 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.

Answer: A
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Re: If two sides of a triangle have lengths 2 and 5, which of th   [#permalink] 27 Nov 2017, 11:19
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