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# Which of the following could be the measures of the sides of a single

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
Which of the following could be the measures of the sides of a single  [#permalink]

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19 Feb 2018, 22:46
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95% (00:28) correct 5% (01:22) wrong based on 37 sessions

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Which of the following could be the measures of the sides of a single triangle?

I. 3, 4, 5
II. 5, 12, 18
III. 3, 3, 3

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

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Posts: 1074
Which of the following could be the measures of the sides of a single  [#permalink]

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20 Feb 2018, 00:14
Bunuel wrote:
Which of the following could be the measures of the sides of a single triangle?

I. 3, 4, 5
II. 5, 12, 18
III. 3, 3, 3

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

As there is a specific rule constraining the lengths of sides of triangles, we'll use it.
This is a Precise approach.

In any triangle, the sum of the length of two sides is greater than the third.
We'll check if the sum of the two shorter sides is larger than the longer one.
I. Since 3 + 4 =7 > 5 then this can be a triangle. (Also, do you recognize what type of triangle this is? Hint: Pythogarean triplets)
II. Since 5 + 12 = 17 < 18, this cannot be a triangle.
III. Since 3 + 3 > 3 this can be a triangle. (In fact, it is equilateral!)

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Re: Which of the following could be the measures of the sides of a single  [#permalink]

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22 Feb 2018, 09:22
Bunuel wrote:
Which of the following could be the measures of the sides of a single triangle?

I. 3, 4, 5
II. 5, 12, 18
III. 3, 3, 3

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

In order for 3 numbers to be the side lengths of a triangle, the sum of any two of them must be greater than the third. In particular, the sum of the two smallest lengths must be greater than the largest length.

I. 3, 4, 5

Since 3 + 4 > 5, they can be the side lengths of a triangle.

II. 5, 12, 18

Since 5 + 12 is not greater than 18, they cannot be the side lengths of a triangle.

III. 3, 3, 3

Since 3 + 3 > 3, they can be the side lengths of a triangle.

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Re: Which of the following could be the measures of the sides of a single   [#permalink] 22 Feb 2018, 09:22
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