Test Your Quant Concepts Chapter 4 - Geometry and Data Analysis

GRE Quant Problem Solving
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I was going through this series and I came across this problem where Greg asked us to find the base of the triangle without using Pythagorean theorem and only two things were given: Height of the triangle i.e. 3 and hypotenuse i.e. 6. It is also a rectangle. Now Greg said because hypotenuse is double the height that means it is a 30-60-90 triangle rule so I want to understand that is it enough to conclude that because hypotenuse is double the height it is a 30-60-90 triangle? I was of the impression that it is other way round like because is it 30-60-90 cases sides are like this. I thought the side being double could just be any other case not necessarily 30-60-90. So, it would be great if you could clear that to me or tell me if we came to this conclusion by using rectangle’s properties?

Thanks!

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You will find that for any right triangle with the hypotenuse being double one of the sides, it will be a 30-60-90 triangle. You can watch a proof video here: https://www.youtube.com/watch?v=SFL4stapeUs

However, for the purposes of the test, just know that the 30-60-90 rule works in both directions.

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Thank you so much!