benjiboo wrote: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.
