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# If the length of side AB is 17, is triangle ABC a right

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Manager
Joined: 26 Dec 2007
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If the length of side AB is 17, is triangle ABC a right [#permalink]

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13 Jan 2008, 15:40
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If the length of side AB is 17, is triangle ABC a right triangle?

(1) The length of side BC is 144.

(2) The length of side AC is 145.

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Manager
Joined: 04 Jan 2008
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Re: DS - Properties of Triangles [#permalink]

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13 Jan 2008, 18:52
We are given just length of one side=17
S1 gives another side, so we can make any triangle with it. sides need not be integer values. so S1 not suffi.

S2 not suffi for same reasons as above

But, taking S1 and S2, we have all three sides of a triangle & using Pythagorean theorem we can see if it is a right triangle.
OA??

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Director
Joined: 09 Jul 2005
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Re: DS - Properties of Triangles [#permalink]

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14 Jan 2008, 08:57
Answer should be C. I followed the same reasoning as Dellin did.

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Intern
Joined: 13 Dec 2007
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Re: DS - Properties of Triangles [#permalink]

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14 Jan 2008, 11:10
Reasoning above is correct, Answer should be C

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VP
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Re: DS - Properties of Triangles [#permalink]

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14 Jan 2008, 11:15
I see 1 and 2 are both insuff by theirselves. together: in order for the triangle to be rectangle we must have ab^2 + bc^2 = ac^2, where obviously ac must be the hypothenuse because it is greatest side. then we know that 145^145=21025. 17^2= 289 and 144^144=20736. 20736+289=21025, then OA is C. anyway, without doing any kind of calculus, by 1 and 2 we would know that it is possible to figure out whether ab^2 + bc^2 = ac^2, so c is suff

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Manager
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Re: DS - Properties of Triangles [#permalink]

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14 Jan 2008, 13:31

OA is C

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SVP
Joined: 04 May 2006
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Schools: CBS, Kellogg
Re: DS - Properties of Triangles [#permalink]

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14 Jan 2008, 21:29
1
KUDOS
marcodonzelli wrote:
I see 1 and 2 are both insuff by theirselves. together: in order for the triangle to be rectangle we must have ab^2 + bc^2 = ac^2, where obviously ac must be the hypothenuse because it is greatest side. then we know that 145^145=21025. 17^2= 289 and 144^144=20736. 20736+289=21025, then OA is C. anyway, without doing any kind of calculus, by 1 and 2 we would know that it is possible to figure out whether ab^2 + bc^2 = ac^2, so c is suff

I'm very lazy, I see that the last digit of the square of 17 plusing the last digit of square of 144 produces a number that ends 5, which is the same as the last digit of square of 145. I conclude that ABC is right triangle at B. So I choose C

Is there any problem with my reasoning?
_________________

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Re: DS - Properties of Triangles   [#permalink] 14 Jan 2008, 21:29
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