Strategy for 3-4-5 right triangles... (quant guys plz help)

[benjiboo]

Does it hold true that, if a right triangle's hypotenuse is a multiple of 5, then the triangle is a "3-4-5 triangle" and thus the legs are in the same ratio?

IE: Can I assume a triangle with a hypotenuse of 25 will have one leg of 15 and the other of 20?

[Viddar]

From what I just calculated, no:
If your hypotenuse is 15 then the other two sides are 10 and 5 by your algorithm but that would violate the Pythagorean theorem, the same is true if the hypotenuse was 30.

I could be wrong, if I am feel free to correct me.

[benjiboo]

update: There is a special right triangle known as 7-24-25, so therefore, the answer to my question is no (as to make sure no one else reading this is wondering)

[Jim@StratusPrep]

Exactly, you must know 2 of the sides.

[Ian Stewart]

Does it hold true that, if a right triangle's hypotenuse is a multiple of 5, then the triangle is a "3-4-5 triangle" and thus the legs are in the same ratio?

Yeah, that's definitely not true, though I have seen one GMAT company make that mistake in a prep video, and I wonder if that's why you're asking (if so, just ignore the video - the math in it is just wrong). As long as numbers work in the Pythagorean Theorem, they can be the sides of a right triangle. So if all you know is that your hypotenuse is 5, yes, the other sides could be 3 and 4, but they could also be 1 and √24, or 2 and √21 or 5√2/2 and 5√2/2 or all kinds of other things.

There's really only one reason to know about 3-4-5 triangles (and 5-12-13 triangles - don't learn any others) for the GMAT, and that's to save a few seconds of calculation when you're given two sides of a right triangle that fit in the 3-4-5 ratio and need to find the third. So if you know, say, the lengths of the legs of a right triangle are 36 and 48, then knowing the 3-4-5 ratio, you can quickly find that the hypotenuse is 60. That said, while this is occasionally tested on the GMAT, it is certainly not frequently tested, and I think many prep books overstate the importance of memorizing these types of things.