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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

 Jan 10, 2018
 #1
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 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

 

 

 

 

cool cool cool

 Jan 10, 2018

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