triangle problem

[ladyazpy]

okay i have a one big triangle and it is cut in half or has a line in the middle which is X, the left side angle is 60 degrees (A side) the right side corner has 30 degrees angle (B sides) and the whole upper pat corner has 90 degrees. (C side
then it say: hint (Area is 1/2 base times height)

here is the question: if an are of tringle ACB is 5 square root of 3? calculate X

 

[Gene]

It sounds like you are describing

       C
      /| .
     / |   .
    /  |x    .
   /   |       .
 A/____|_________B
       D

So you have three 30°-60°-90° triangles.
AD = x/sqrt(3)
AC = 2*AD
AB = 2*AC
x*AB/2= 5*sqrt(3)

 

[ladyazpy]

t

i appreciate that you show me how to solve each sides my major problem is how can i solve for the x/sqrt(3)
if i have mo idea what x is

 

[Gene]

AD = x/sqrt(3)
AC = 2*AD = 2x/sqrt(3)
AB = 2*AC = 4x/sqrt(3)
x*AB/2 = x*(4x/sqrt(3))/2 = 5*sqrt(3)
So
2x²/sqrt(3) = 5*sqrt(3)
and you can solve that for x

 

[ladyazpy]

hi i think i got the answer

so..
i got

x= square root of 5/2 is this right?

 

[Gene]

'Fraid not.
2x²/sqrt(3) = 5*sqrt(3)
Multiply both sides by sqrt(3) to get
2x²=5*3=15

 

[Denis]

You're close, ladysoso:

2x^2 / sqrt(3) = 5sqrt(3)

2x^2 = sqrt(3) * 5sqrt(3)

Since sqrt(3) * sqrt(3) = 3, then right side = 15 ; OK??

 

[ladyazpy]

so okay i got the steps but what's gonna happen to 2X square

are you suppose to divide it by 2 so its gonna be 15/2 = X squared, the you take the square root?

 

[Denis]

YES.
2x^2 = 15
x^2 = 15/2
x = sqrt(15/2)

"so okay i got the steps but what's gonna happen to 2X square"
In the future, PLEASE write "2X square" this way: 2x^2