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Is the perimeter of triangle T greater than the perimeter of

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Is the perimeter of triangle T greater than the perimeter of [#permalink] New post 02 Jul 2010, 12:38
00:00
A
B
C
D
E

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Question Stats:

50% (01:43) correct 50% (00:51) wrong based on 42 sessions
Is the perimeter of triangle T greater than the perimeter of square S?

(1) T is an isoceles right triangle.
(2) The length of the longest side of T is equal to the length of a diagonal of S.
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jun 2013, 04:58, edited 2 times in total.
Edited the question and added the OA
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Re: Triangles and Squares - comparing perimeter [#permalink] New post 02 Jul 2010, 12:40
Expert's post
knewtonina wrote:
I'm stumped on this one. Can anyone help?

Is the perimeter of triangle T greater than the perimeter of square S ?
(1) T is an isoceles right triangle.
(2) The length of the longest side of T is equal to the length of a diagonal of S.


(1) T is an isoceles right triangle --> no info about the square. Not sufficient.

(2) The length of the longest side of T is equal to the length of a diagonal of S --> let the side of the square be s --> the longest side of the triangle will be \sqrt{2}s and P_{square}=4s. Now the max perimeter of the triangle T will be if this triangle is equilateral, then P_{triangle}=3\sqrt{2}s>4s=P_{square}, but if triangle T is half of the square S (isosceles right triangle), then P_{triangle}=\sqrt{2}s+s+s=s(\sqrt{2}+2)<4s=P_{square}. Two different answers. Not sufficient.

(1)+(2) Statement (1) says that we have the second case from statement (2), hence P_{triangle}=\sqrt{2}s+s+s=s(\sqrt{2}+2)<4s=P_{square}. Sufficient.

Answer: C.

Hope it's clear.
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Re: Triangles and Squares - comparing perimeter [#permalink] New post 02 Jul 2010, 21:07
I get B

i). Not sufficient

ii). a - longest side of triangle
x - side of square
Given, a = sqrt(2)*x, so perimeter of square, 4x = 2*sqrt(2)*a
Perimeter of triangle (of sides a,b,c) = a+b+c is < 2a (sum of the two sides (b+c) < a)

So, B is sufficient
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Re: Triangles and Squares - comparing perimeter [#permalink] New post 05 Jul 2010, 07:03
Hi dallasgmat,

Note:
- In triangles, sum of any two sides is GREATER than the third side.
- In triangles, difference of any two sides is LESS than the third side.

Keep in mind the above to avoid concept mistakes.

cheers,
Jack
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Re: Triangles and Squares - comparing perimeter [#permalink] New post 24 May 2011, 07:38
Is the perimeter of triangle T greater than the perimeter of square S ?
(1) T is an isosceles right triangle.
(2) The length of the longest side of T is equal to the length of a diagonal of S.

Solution:
Bunnuel is right the ans is C.
(1) No information about S is given, so insufficient
(2) Let the one side of s = x, so Diagonal of s = x√2
Perimeter of S = 4x
Thus, the longest side of T = x√2
No other information is given about other sides of T, So insufficient.

Considering C
the sides of T = x, x, x√2 [Sides of triangle with 90 degree, 45 degree and 45 degree is s, s, s√2]
Perimeter of T = x + x + x√2 which is Less than 4x.
Ans. C
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Re: perimeter of triangle T greater than the perimeter of square [#permalink] New post 09 Feb 2012, 20:09
subhajeet wrote:
Is the perimeter of triangle T greater than the perimeter of square S ?

(1) T is an isoceles right triangle.

(2) The length of the longest side of T is equal to the length of a diagonal of S.


(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can anyone please provide a solution for this.


Let a, b, and c denote the three sides of triangle T, with c as the largest side, and let s denote a side of square S.
The question then becomes: is (a+b+c)>4s?

(1) Does not give any information about the square S. Thus, Not Sufficient.

(2) c = s\sqrt{2}.
From the triangle property, we know that sum of lengths of any two sides of a triangle is always greater than the length of third side. Thus, for triangle T, we have:
a+b>c
a+b+c>2c
a+b+c> 2\sqrt{2}s
This still is insufficient data, as we cannot prove weather
4s>(a+b+c)>2\sqrt{2}s OR
(a+b+c)>4s (true in case of equilateral triangles)

(1)+(2) a = b, and c = a\sqrt{2} = s\sqrt{2}
Thus, we get a = s.
a+b+c = a(2+\sqrt{2}) < 4s. Thus, we can have our answer to the question: is (a+b+c)>4s? No!

So correct answer is (C): (1) and (2) are sufficient together, but not alone..

:)

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Re: perimeter of triangle T greater than the perimeter of square [#permalink] New post 09 Feb 2012, 22:41
Expert's post
subhajeet wrote:
Is the perimeter of triangle T greater than the perimeter of square S ?

(1) T is an isoceles right triangle.
(2) The length of the longest side of T is equal to the length of a diagonal of S.

Can anyone please provide a solution for this.


Merging similar topics. Please ask if anything remains unclear.
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Re: Is the perimeter of triangle T greater than the perimeter of [#permalink] New post 10 Feb 2012, 04:24
Bunnel thanks for the explanation :)
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Re: Is the perimeter of triangle T greater than the perimeter of [#permalink] New post 10 Feb 2012, 04:58
Again! Well done explained! Couldn´t figure it out myself! :(
Re: Is the perimeter of triangle T greater than the perimeter of   [#permalink] 10 Feb 2012, 04:58
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