(Originais Teachy 2023) - Question Hard of Mathematics

In a sustainable construction project, an engineer needs to calculate the amount of material needed to cover the external surface of a structure. The area to be covered is represented by the expression (4 + 2√6) m^2. The coating material is sold in rolls with a width of 2 meters and a length of 20 meters. To optimize the use of the material, the engineer wants to cut the rolls in a way that the width of the material is an integer multiple of √6 meters. The first step of this process is to determine what should be the width, in meters, of each strip of material to be cut from the roll. To rationalize the calculation, the engineer needs to express the width of the strip in terms of √6 and integers. What is the width, in meters, of each strip of material that the engineer should cut from the roll? Justify your answer by rationalizing the denominator of the fraction that represents the width of the strip of material.