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Geometry - right angle

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Sat Apr 03, 2010 11:12 am

I have a general question. If the hypotenuse of a right triangle is 5, can I assume that the other 2 sides are 3 & 4 (doesn't matter which one is base or height). Similary if I know one side is 3, can I assume other side is 4 and hypotenuse is 5.

Will appreciate a response.

Vineet

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Source: Beat The GMAT — Problem Solving | Sat Apr 03, 2010 11:12 am

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Sat Apr 03, 2010 11:26 am

If you know any two sides then only can you assume the third. If you know 3 and 5, then definitely the other one is 4.

Ill give you an example
If you find one side 3, you cannot assume the rest to be 4 and 5
Another case may be (3,3,3root2) which is multiple of another common triplet 1,1,root2

Similarly for others
Hope that helps

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Sat Apr 03, 2010 11:41 am

eaakbari wrote:If you know any two sides then only can you assume the third. If you know 3 and 5, then definitely the other one is 4.

Ill give you an example
If you find one side 3, you cannot assume the rest to be 4 and 5
Another case may be (3,3,3root2) which is multiple of another common triplet 1,1,root2

Similarly for others
Hope that helps

Ditto !

I think unless until specified that measures of all the sides are integers, we cannot assume that the other two will be 3 and 4 when the hypotenuse is 5. If all the sides are integers, then yes, we can conclude that the triplet should be 5,4, and 3.

Regards,
Harsha

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Apr 03, 2010 11:53 am

vineetbatra wrote:I have a general question. If the hypotenuse of a right triangle is 5, can I assume that the other 2 sides are 3 & 4 (doesn't matter which one is base or height). Similary if I know one side is 3, can I assume other side is 4 and hypotenuse is 5.

Will appreciate a response.

Vineet

as the angle changes with same hypotenuous the altitude and base changes
see diagram

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right angle.xls: (13.5 KiB) Downloaded 71 times

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Sat Apr 03, 2010 5:20 pm

Thanks guys, that makes sense.

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