Let x be the length of a diagonal of a face of a cube and y be the length of a diagonal of the cube. If x + y = (5 + 2\sqrt{6}) units, then what is the total surface area of the cube ?

Explanation

Let edge be a. Then x = a\sqrt{2} and y = a\sqrt{3}. Given a(\sqrt{2}+\sqrt{3}) = 5+2\sqrt{6} = (\sqrt{2}+\sqrt{3})^2, we find a = \sqrt{2}+\sqrt{3}. The surface area is 6a^2 = 6(5+2\sqrt{6}) = 6(x+y).

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