Tricky Triangle

Geometry Level 4

XX , YY and ZZ are 3 mutually parallel straight lines in a plane, such that YY is between XX and ZZ and the distance between XX and YY is 1010 units and the distance between YY and ZZ is 66 units. ABCABC is an equilateral triangle with AA on XX , BB on YY and CC on ZZ. If the area of ABC\triangle ABC can be expressed as a2b\dfrac{a^2}{\sqrt{b}} where aa and bb are coprime positive integers and bb is not divisible by the square of any prime, find the value of a+ba+b.

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