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perimeter of triangle GT Perimeter of Square S

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perimeter of triangle GT Perimeter of Square S

by M811 » Wed May 12, 2010 6:04 pm
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.



[spoiler]Ans : C[/spoiler]
Last edited by M811 on Wed May 12, 2010 6:49 pm, edited 1 time in total.
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by liferocks » Wed May 12, 2010 6:27 pm
Clearly 1 alone is not sufficient as it does not provode any relation between the sides of the triangle and square.

From 2
if the length of the sides of the square is a..diagonal aV2

longest side of triangle is aV2...perimeter will be maximum when the triangle is equilateral with side aV2

in that case perimeter is 3aV2 or approximately 4.2a>perimeter of square(4a)
if the triangle is an isoceles right triangle perimeter =aV2(V2+1)<4a...insufficient

together
perimeter of T=aV2(V2+1)
perimeter of S=4a
hence perimeter of triangle T is less than the perimeter of square S..sufficient

Ans option C

please use spoiler for OA.
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by arora007 » Wed Aug 11, 2010 9:19 pm
I fail to agree with the OA, I think its E.

we are clear thats its a C or E case, wont go into its details...


now, the perimeter of square is 2root2 t = 2.82t

THE TWIST, the question is written in such a manner that its not clear that the longest sides is the congruent part or not the congrument part....

If I consider a case of congruent part the the 2 sides are t+t = 2t
and the third side is something less than t

so, the triangle perimeter is less than 3t but greater than 2t in any circumstance.

thus it can be greater than 2.82t or less than 2.82t , thus I conclude E.

Can Experts please confirm ??
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by kvcpk » Wed Aug 11, 2010 9:55 pm
arora007 wrote:I fail to agree with the OA, I think its E.

we are clear thats its a C or E case, wont go into its details...


now, the perimeter of square is 2root2 t = 2.82t

THE TWIST, the question is written in such a manner that its not clear that the longest sides is the congruent part or not the congrument part....

If I consider a case of congruent part the the 2 sides are t+t = 2t
and the third side is something less than t

so, the triangle perimeter is less than 3t but greater than 2t in any circumstance.

thus it can be greater than 2.82t or less than 2.82t , thus I conclude E.

Can Experts please confirm ??
Hi Arora,

I think you have missed that T is Isoceles Right Triangle.
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by arora007 » Wed Aug 11, 2010 10:26 pm
kvcpk wrote:
arora007 wrote:I fail to agree with the OA, I think its E.

we are clear thats its a C or E case, wont go into its details...


now, the perimeter of square is 2root2 t = 2.82t

THE TWIST, the question is written in such a manner that its not clear that the longest sides is the congruent part or not the congrument part....

If I consider a case of congruent part the the 2 sides are t+t = 2t
and the third side is something less than t

so, the triangle perimeter is less than 3t but greater than 2t in any circumstance.

thus it can be greater than 2.82t or less than 2.82t , thus I conclude E.

Can Experts please confirm ??
Hi Arora,

I think you have missed that T is Isoceles Right Triangle.
u are right!
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