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A certain right triangle has sides of length x, y and z, where x < y <

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A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 06 Jul 2017, 02:11
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Question Stats:

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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 06 Jul 2017, 02:12
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Bunuel wrote:
A certain right triangle has sides of length x, y and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of z?

(A) z > 2
(B) √2 < z < 2
(C) √2 < z < √3
(D) 1 < z < √2
(E) z < 1


This is a modified question of the the following OG question: https://gmatclub.com/forum/a-certain-ri ... 68727.html
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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 06 Jul 2017, 02:37
Bunuel wrote:
A certain right triangle has sides of length x, y and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of z?

(A) z > 2
(B) √2 < z < 2
(C) √2 < z < √3
(D) 1 < z < √2
(E) z < 1


Right triangle has sides x, y, z and z being the highest must be Hypotenuse

i.e. (1/2)*x*y = 1
i.e. x*y = 1
@\(y_{min}\) , x must be maximum and z must be Minimum
and then first unacceptable solution will be
@x = y, i.e. \(y^2 = 2\)
@x = y, i.e. \(y = \sqrt{2}\)

@x=y. \(z_{min} = 2\)

but since x<y, therefore z must be greater than 2

Answer: option A
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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 06 Jul 2017, 02:38
Bunuel wrote:
A certain right triangle has sides of length x, y and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of z?

(A) z > 2
(B) √2 < z < 2
(C) √2 < z < √3
(D) 1 < z < √2
(E) z < 1


ALTERNATIVELY

Take any random case

i.e. x = 1/8, y = 16 and calculate z i.e. z > 16

All options eliminated except the first option

Answer: Option A
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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 08 Jul 2017, 10:52
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the answer is A.

since we know that area is 1 and it is given that x < y < z for the right angled triangle, we can say that z is the longest triangle. x*y = 2. let's say y(2) > x(1), then z>2.
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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 30 Jul 2017, 06:27
brs1cob wrote:
the answer is A.

since we know that area is 1 and it is given that x < y < z for the right angled triangle, we can say that z is the longest triangle. x*y = 2. let's say y(2) > x(1), then z>2.


Hi brs1cob,

I do understand your approach, though I had a doubt.
For any given triangle if two sides are given then the third side has to be less than the sum and greater than the difference of the two sides.
So in the current case since xy=2, if we take x =1, y=2, then the value of z can only be greater than 1 and less than 3.

Where am I going wrong?

Thanks!
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Re: A certain right triangle has sides of length x, y and z, where x < y <  [#permalink]

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New post 09 Aug 2019, 08:56
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Re: A certain right triangle has sides of length x, y and z, where x < y <   [#permalink] 09 Aug 2019, 08:56
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