Doubt in Geometry question

GRE Quant Problem Solving
1

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Why are we not using Pythagoras triplets here? The triangle is right-angled. Hypotenuse is 5. Can we not consider the triplet and area will be 6?
The answer here has been derived from 30-60-90 rule. Answer = 5.34
Kindly reason.

This is one of the one-month study plan’s questions solved in Dedicated Geometry Session 4.

2

Does a 3-4-5 triangle follow the side ratios required by a 30-60-90 triangle?

3

Okay, not exactly, it’s around 90-53-36.

4

Yeah, important lesson. The triplets dont follow the ratios for 90-45-45 or 30-60-90 triangles