2001 AIME I Problem 5

An equilateral triangle is inscribed in the ellipse whose equation is x^2+4y^2=4. One vertex of the triangle is (0,1), one altitude is contained in the y-axis, and the length of each side is \sqrt{\frac mn}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.