Triplet Confusion !

[mmslf75]

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 ?

[mp2437]

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).

[Stacey Koprince]

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.

[Stuart@KaplanGMAT]

>>>>> 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.