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Is the perimeter of triangle T greater than the perimeter of square S?

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Mbawarrior01
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Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   Updated on: 17 Jul 2016, 09:06
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Is the perimeter of triangle T greater than the perimeter of square S?

(1) The length of the longest side of T is twice the length of a side of S.

(2) T is isosceles.


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Source : Jeff Sackmann
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A

Originally posted by Mbawarrior01 on 17 Jul 2016, 08:46.
Last edited by Bunuel on 17 Jul 2016, 09:06, edited 1 time in total.
Edited the question.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   17 Jul 2016, 09:05
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Is the perimeter of triangle T greater than the perimeter of square S?

Say the lengths of the sides of the triangle are a, b and c (where \(a \geq b \geq c\)) and the length of a side of the square is x. So, the question asks whether a + b + c > 4x.

(1) The length of the longest side of T is twice the length of a side of S --> a = 2x. The question becomes is a + b + c > 2a --> is b + c > a. We know that 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. According to this property we know that b + c > a must be true. Sufficient.

(2) T is isosceles. We know nothing about the square. Not sufficient.

Answer: A.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   17 Jul 2016, 09:06
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Bunuel wrote:
Is the perimeter of triangle T greater than the perimeter of square S?

Say the lengths of the sides of the triangle are a, b and c (where \(a \geq b \geq c\)) and the length of a side of the square is x. So, the question asks whether a + b + c > 4x.

(1) The length of the longest side of T is twice the length of a side of S --> a = 2x. The question becomes is a + b + c > 2a --> is b + c > a. We know that 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. According to this property we know that b + c > a must be true. Sufficient.

(2) T is isosceles. We know nothing about the square. Not sufficient.

Answer: A.


Similar question to practice: is-the-perimeter-of-triangle-t-greater-than-the-perimeter-of-96639.html
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   17 Jul 2016, 11:16
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aditi2013 wrote:
Is the perimeter of triangle T greater than the perimeter of square S?

(1) The length of the longest side of T is twice the length of a side of S.

(2) T is isosceles.


Show Spoiler
Source : Jeff Sackmann


Question is if sum of three sides of triangle> sum of 4 sides of square or 4S

(1) The length of the longest side of T is twice the length of a side of S.

Length of longest side = 2S (if length of side of square= S)

Length of longest side +length of other two sides
2S + >2S (Sum of two sides of triangle is always > third side)

>4S

Hence Sufficient.

(2) T is isosceles.
Not sufficient

A is the answer
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   02 Aug 2018, 19:21
Mbawarrior01 wrote:
Is the perimeter of triangle T greater than the perimeter of square S?

(1) The length of the longest side of T is twice the length of a side of S.

(2) T is isosceles.


Show Spoiler
Source : Jeff Sackmann


(2) gives us nothing

(1) is sufficient, because:
Side of triangle = 2a ---> side of square is a ---> the perimetr of the square = 4a
We know that sum of any 2 sides of the triangle is greater than any other side of this triangle, it means:
b+c>2a ---> perimetr = 2a+b+c > 4a ---> suff
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Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   Updated on: 15 Aug 2018, 11:57
Bunuel

if a=2x , then how you replaced x by 2a ? it should be a/2 ?

please help me understand.

Originally posted by boomerangbak on 15 Aug 2018, 11:55.
Last edited by boomerangbak on 15 Aug 2018, 11:57, edited 1 time in total.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   15 Aug 2018, 11:56
Bunuel

if a=2x , then how you replaced x by 2a ? it should be a/2 ?

please help me understand.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   15 Aug 2018, 15:31
boomerangbak wrote:
Bunuel

if a=2x , then how you replaced x by 2a ? it should be a/2 ?

please help me understand.


Bunuel did not replace x by 2a. He replaced 4x by 2a. So it is all good.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   16 Aug 2018, 01:41
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boomerangbak wrote:
Bunuel

if a=2x , then how you replaced x by 2a ? it should be a/2 ?

please help me understand.

__________________
a = 2x, so 4x = 2a.
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink] New post   07 Sep 2021, 18:07
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Re: Is the perimeter of triangle T greater than the perimeter of square S? [#permalink]
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