Question 1106512
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{{{y^4-3y^2-270 = (y^2-18)(y^2+15) = 0}}}<br>
{{{y^2=18}}} or {{{y^2 = -15}}}.<br>
Obviously we need to choose the positive real root.<br>
So the height of the equilateral triangle is {{{3*sqrt(2)}}}.<br>
The altitude of the equilateral triangle divides the triangle into two 30-60-90 right triangles.  So the length of one-half the base is {{{(3*sqrt(2))/sqrt(3)}}}.<br>
Then the area of the triangle is one-half base times height:
{{{((3*sqrt(2))/sqrt(3))*(3*sqrt(2)) = 18/sqrt(3) = 6*sqrt(3)}}}