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

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If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 06:39
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-length-of-side-ab-is-17-is-triangle-abc-a-right-tria-127069.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2015, 03:32, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 10:00
I don't see other possibility...

C should be correct... but would it be a GMAT question? i mean... calculating 144², 145² takes time...
generally GMAT does not like spending too much time making calculations...

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 10:12

I see that 17-square + 144-square = 145

so knowing that BC is 144 is sufficient

also knowing that 145 is sufficient by itself
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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 10:16
pierrealexandre77 wrote:
I don't see other possibility...

C should be correct... but would it be a GMAT question? i mean... calculating 144², 145² takes time...
generally GMAT does not like spending too much time making calculations...

you may be correct than GMAT wont ask questions involving such numbers but then
" HOPE FOR THE BEST,PREPARE FOR THE WORST"

Also 145^2 will be equal to 144^2 + (144*2 +1)----this is same as 144^2 plus 17^2

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 10:21
srini123 wrote:

I see that 17-square + 144-square = 145

so knowing that BC is 144 is sufficient

also knowing that 145 is sufficient by itself

but option 1 or 2 do not tell anything about the other side...the 3rd side of triangle... we can consider the 3rd (unknown side) as the one with maximum length e.g. 147 then also it will hold true by logic that sum of 2 sides should be more than the longest side....

where am I goofing on this

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 10:27
astermatrix must be right, it has to be C.

we need to know both the other sides
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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 11:49
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srini123 wrote:
astermatrix must be right, it has to be C.

we need to know both the other sides

OA is C
With all 3 sides you could see if a^2 + b^2 = c^2

As per above discussion, I agree it would be impossible in the 2 minutes provided to determine if this is a right triangle. However since this is a yes/no DS question we don't need to find an answer. Can we find an answer yes? Is this actually a right triangle? Who cares!

For those interested however... it is a right triangle.

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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13 Oct 2009, 12:09
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As asterixmatrix pointed out, this doesnt involve a whole lot of crazy calculation if you notice that 145^2 - 144^2 = (145-144)*(145+144) = 1*289 = 17^2.

You still need both those values to know whether it is a right triangle so answer should be [C].

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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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29 Jun 2015, 11:43
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Re: If the length of side AB is 17, is triangle ABC a right triangle? [#permalink]

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30 Jun 2015, 03:32
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hogann wrote:
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.

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

(1) The length of side BC is 144 --> there are infinitely many triangles possible with the sides of 17 and 144, two of them will be right triangles (17^2+144^2=x^2, where x is a hypotenuse and 17^2+y^2=144^2, where y is an another leg) and others will not. Not sufficient.

(2) The length of side AC is 145. Not sufficient for the same reason.

(1)+(2) We know all the sides hence, even without actual calculation, we can find out whether the triangle is right or not. Sufficient. (As a matter of fact it is a right triangle: 17^2+144^2=145^2)

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-length-of-side-ab-is-17-is-triangle-abc-a-right-tria-127069.html
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Re: If the length of side AB is 17, is triangle ABC a right triangle?   [#permalink] 30 Jun 2015, 03:32
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