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by bblast » Mon Jul 18, 2011 10:24 am
In triangle xyz, what is the length of yz ?


1>xy=3
2>xz=5.





Cant we assume it to be a 3-4-5 ? are there other values possible. I know about the theorem that sum of 2 sides is greater than 3rd side and the mod of diff between 2 sides is less than the 3rd side. So if we apply this here, are non integer values possible for yz ????
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by winniethepooh » Mon Jul 18, 2011 10:34 am
A bit confused, the statement is x-y or x*y?
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by bblast » Mon Jul 18, 2011 10:40 am
winniethepooh wrote:A bit confused, the statement is x-y or x*y?
Hi,

The statements are lengths of the sides of the triangle.
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by winniethepooh » Mon Jul 18, 2011 10:56 am
The answer should be E.
By both the statements you get no certainty of length of yz, as yz can be anywhere from 2<yz<8.
So, E!
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by Frankenstein » Mon Jul 18, 2011 8:18 pm
bblast wrote:In triangle xyz, what is the length of yz ?

1>xy=3
2>xz=5.


Cant we assume it to be a 3-4-5 ? are there other values possible. I know about the theorem that sum of 2 sides is greater than 3rd side and the mod of diff between 2 sides is less than the 3rd side. So if we apply this here, are non integer values possible for yz ????
Hi,
You cannot assume it to be 3-4-5. Third side can be any value between 2 and 8. Non- integers are possible. If you are not convinced, just consider a right triangle with legs as 3 and 5. Hypotenuse will be sqrt(5^2+3^2) = sqrt(34) --> Non- integer(in fact irrational). So, depending on the angle between XY and XZ, the length of YZ lies between 2 to 8 (exclusive).
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by bblast » Mon Jul 18, 2011 9:31 pm
thanks Frank,

i just realized I have made this mistake twice now. The other time I took the sum of 2 legs of a right triangle = 7 as sufficient.

however any combination of length is possible.
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by amit2k9 » Mon Jul 18, 2011 11:00 pm
using a+b,

xz-xy < yz < xz + xy

5-3 < yz < 8

hence E it is.
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