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Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is

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Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is [#permalink]

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New post Updated on: 14 Sep 2017, 04:41
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Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is the area of ABC?

A) √2
B) 2
C) 2√2
D) √3/4
E) √15/2

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Originally posted by Mehed iHasan on 14 Sep 2017, 04:32.
Last edited by Bunuel on 14 Sep 2017, 04:41, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is [#permalink]

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New post 14 Sep 2017, 09:32
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Mehed iHasan wrote:
Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is the area of ABC?

A) √2
B) 2
C) 2√2
D) √3/4
E) √15/2


In any triangle sum of two sides is greater than the third side.
Here \(z+\sqrt{z}\) will never be greater than \(z^2\) as \(z\) is a positive integer; except for one possible solution.
The only possible solution is \(\sqrt{z}=z=z^2=1\).
That is the triangle is equilateral. Hence the area will be \(\sqrt{3}/4\)

Option D
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Re: Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is [#permalink]

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New post 14 Sep 2017, 10:38
only possible value of Z is 1 ..(Sum of two sides of triangle must be greater than 3rd side)
It forms a equilateral triangle

Area = √3/4
Re: Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is   [#permalink] 14 Sep 2017, 10:38
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Triangle ABC has sides Z, √Z and Z^2, where Z is an integer. What is

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