Problem #1828
1828.

Three congruent isosceles triangles are constructed with their bases on the sides of an equilateral triangle of side length . The sum of the areas of the three isosceles triangles is the same as the area of the equilateral triangle. What is the length of one of the two congruent sides of one of the isosceles triangles?
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Instructions for entering answers:
 Reduce fractions to
lowest terms and enter in the form 7/9.
 Numbers involving pi should be written as 7pi or 7pi/3
as appropriate.
 Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
 Exponents should be entered in the form 10^10.
 If the problem is multiple choice, enter the appropriate
(capital) letter.
 Enter points with parentheses, like so: (4,5)
 Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
NOT 0+2i).
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