Triplet Confusion !

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mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pmFollowed by: 2 members; Thanked: 31 times

by mmslf75 » Wed Nov 25, 2009 9:03 am

Hi Please help on this one ...

>>>>> For a triangle with one of its sides as 5 and Angle 90 degress,

Does it necessarily mean that other two sides be 3 and 4 ?

OR

That the other two sides maybe [5/root of 2] and [5/root of 2]

>>>>> If it were stated that the numbers are integers and one side is 5 and angle 90 degrees; then would it necessariy mean that other sides are 3 and 4 ?

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Source: Beat The GMAT — Problem Solving | Wed Nov 25, 2009 9:03 am

mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Wed Nov 25, 2009 9:40 am

Do you know if 5 is the hypotenuse? If it is, and you know that each side has to be an integer, than x^2 + y^2 = z^2, where z = 5 can only hold for (3,4,5).

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Stacey Koprince: GMAT Instructor; Posts: 2228; Joined: Wed Dec 27, 2006 3:28 pmFollowed by: 694 members; Location: Montreal, Canada; Thanked: 639 times; GMAT Score:780

by Stacey Koprince » Wed Dec 02, 2009 1:54 pm

mp has it right. If you know that 5 is the hypotenuse, and that the other two sides have integer lengths, then the two legs are 3 and 4.

If you don't know whether 5 is the hypotenuse, or if you don't know that the two legs have integer lengths, then you don't know the lengths of the other two sides.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Dec 02, 2009 7:39 pm

mmslf75 wrote: >>>>> If it were stated that the numbers are integers and one side is 5 and angle 90 degrees; then would it necessariy mean that other sides are 3 and 4 ?

Without knowing whether the 5 side is the hypotenuse, that isn't enough information to prove 3/4/5, since 5/12/13 would also be possible.

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