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If the height of an equilateral triangle is also a root of the equation y4-3y2-270, then the area of the triangle, in cm2 is,

 

A) \(8√2\)

B) \(6√3\)

C)\(12√2\)
D)\(9√3\)

E)\(3√6\)

jonathanxu999  Jan 16, 2018
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2+0 Answers

 #1
avatar+85623 
+2

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

 

(y^2 - 18)  (y^2 + 15)  =  0

 

Only the first factor will result in a real (positive) answer

 

So

 

x^2  - 18  = 0

 

x^2  =  18          take the positive root

 

x  = √18    

 

√3  =  x / (3/√2)

 

And because we have an equilateral triangle we can find  (1/2) base ,x,  thusly

 

tan 60  = √18/ x   ⇒   x  =  √18/tan (60)  

 

So.....the area  is  

 

(1/2)base  * (height)   =

 

√18 * √18  /  tan (60)  =

 

18    / √3   =  

 

18√3/ 3  =

 

6√3  units^2

 

 

cool cool cool

CPhill  Jan 16, 2018
 #2
avatar+113 
+2

thanks

jonathanxu999  Jan 20, 2018

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