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# Is the perimeter of a triangle greater than 30?

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Intern
Joined: 18 Apr 2013
Posts: 33
Is the perimeter of a triangle greater than 30?  [#permalink]

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06 Jul 2017, 08:07
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Difficulty:

65% (hard)

Question Stats:

43% (01:00) correct 57% (01:13) wrong based on 72 sessions

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Is the perimeter of a triangle greater than 30?
1) The shortest side's length is greater than 10.
2) The longest side's length is greater than 15.
Intern
Joined: 01 May 2017
Posts: 32
Re: Is the perimeter of a triangle greater than 30?  [#permalink]

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06 Jul 2017, 10:17
1
Statement 1: let x= shortest side. x>10 let's say 10.1
Let y and z be the other two side. Thus y>10.1 say 10.2 & z>10.1 say 10.3,(because each of the sides must be greater than the shortest side.)

Perimeter, P =x +y +z.

P =10.1 + 10.2 + 10.3 =30.6. Thus P>30

This will be the case in each situation. SUFFICIENT

Statement 2: let x= longest side. x>15.
Let y and z be the other two side. Thus y + z >15(because sum of any two sides of a triangle is greater than the third side.)

Perimeter, P =x +y +z. Thus P >30.

This will be the case in each situation. SUFFICIENT

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Director
Joined: 02 Sep 2016
Posts: 740
Re: Is the perimeter of a triangle greater than 30?  [#permalink]

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06 Jul 2017, 12:03
Great question.

Got stuck with some values here that goes against the rule (sum of two sides > third side)

1) Sufficient
2) I assumed:
a>15
Least value of a=16

And took b =c = 15

Yes

But when I took a=16 and b=c=4

No.

But the second case cannot be true.
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Joined: 12 Nov 2016
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Re: Is the perimeter of a triangle greater than 30?  [#permalink]

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08 Sep 2017, 00:53
1
roastedchips wrote:
Is the perimeter of a triangle greater than 30?
1) The shortest side's length is greater than 10.
2) The longest side's length is greater than 15.

St 1

Yes because if we even minimized the perimeter by making the triangle an equilateral triangle for example -11-11-11 then it would be greater than 30

St 2

A +B > C therefore the sum of A and B must be greater than C and if c is greater than 15 then the perimeter will be greater than 15

D
Re: Is the perimeter of a triangle greater than 30? &nbs [#permalink] 08 Sep 2017, 00:53
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