If the height of an equilateral triangle is also a root of the equation y^4-3y^2-270,
then the area of the triangle, in cm^2, is
y^4 - 3y^2 - 270 = 0 factor
( y^2 - 18) (y^2 + 15) = 0
Only the first factor provides the real solution of y = √18 cm = height of the triangle
And...since the altitude of this triangle sets up a 30-60-90 triangle, the side of the equilateral triangle = 2√18 / √3 = 2√6 = √24 cm
So....the area of this triangle is =
(1/2)base * height =
(1/2)√24 * √18
(1/2) 2√6 * 3√2 =
3√12 =
6 √3 cm ^ 2