Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 years ago

If the height of an equilateral triangle is also a root pf the equation y^4-3y^2-270, then the area of the triangle is?

2 Answers

Relevance
  • Favorite Answer

    y^4 - 3y^2 - 270 = 0

    y^2 = (3 +/- sqrt(9 + 1080)) / 2

    y^2 = (3 +/- sqrt(1089)) / 2

    y^2 = (3 +/- 33) / 2

    y^2 > 0

    y^2 = (3 + 33) / 2

    y^2 = 36/2

    y^2 = 18

    y = +/- 3 * sqrt(2)

    y = 3 * sqrt(2)

    So, the height is equal to 3 * sqrt(2)

    (s/2)^2 + h^2 = s^2

    (s/2)^2 + 18 = s^2

    s^2 / 4 + 18 = s^2

    18 = (3/4) * s^2

    18 * (4/3) = s^2

    24 = s^2

    2 * sqrt(6) = s

    A = (1/2) * s * h

    A = (1/2) * 2 * sqrt(6) * sqrt(18)

    A = sqrt(6) * sqrt(6) * sqrt(3)

    A = 6 * sqrt(3)

  • 2 years ago

    y^4-3y^2-270=0

    =>

    y^2=18 (take +ve root only)

    =>

    y=3sqr(2) (take +ve root only)

    Let a be the side-length of the triangle, then

    asin(60*)=3sqr(2)

    =>

    a=2sqr(6)

    =>

    the area of the triangle=

    2sqr(6)*3sqr(2)/2=6sqr(3)

Still have questions? Get your answers by asking now.