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Two sides of triangle given, what's possible perimeter?

This topic has 1 expert reply and 4 member replies

Two sides of triangle given, what's possible perimeter?

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If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter?
I. 9
II. 15
III. 19

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

OA: A

Please explain...

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Master | Next Rank: 500 Posts Default Avatar
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The 3rd side of a triangle has to be less than the sum of the other two sides, and more than their difference.

So in our case the 3rd side is 3< s < 7

Perimeter = 2+5+s

assume s = 3 perimeter = 10

assume s = 7 perimeter = 14


So none of the given answers work out as the perimeter has to be > 10 and < 14

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phoenixhazard wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter?
I. 9
II. 15
III. 19

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

OA: A

Please explain...
The third side rule of triangles:

The third side of a triangle must be less than the sum of the other 2 sides and bigger than the difference of the other 2 sides.

Thus, given a side of 2, a side of 5, and a third side s:
5-2 < s < 5+2
3 < s < 7.

Let p = perimeter.
If s=3, p = 3+2+5 = 10.
If s=7, p = 7+2+5 = 14.
The values above give the range of the perimeter. Since 3 < s < 7, we know that 10 < p < 14.

Since none of the given perimeters are between 10 and 14, the correct answer is A.

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Thanks! I didn't know that rule

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N:Dure wrote:
The 3rd side of a triangle has to be less than the sum of the other two sides, and more than their difference.

It is a very important rule in the case of Triangles,
Thanks for posting the rule, I almost forgot.......

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GMATGuruNY wrote:
phoenixhazard wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter?
I. 9
II. 15
III. 19

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

OA: A

Please explain...
The third side rule of triangles:

The third side of a triangle must be less than the sum of the other 2 sides and bigger than the difference of the other 2 sides.

Thus, given a side of 2, a side of 5, and a third side s:
5-2 < s < 5+2
3 < s < 7.

Let p = perimeter.
If s=3, p = 3+2+5 = 10.
If s=7, p = 7+2+5 = 14.
The values above give the range of the perimeter. Since 3 < s < 7, we know that 10 < p < 14.

Since none of the given perimeters are between 10 and 14, the correct answer is A.
is it greater than or equal to or simply greater than ?

Please confirm so that i can get my basic strong .

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