SOLUTION: Please help me solve this word problem: There is a 30-60-90 triangle with an area of 24 radical 3. What is the perimeter of this triangle, and what are the side lengths? (All in

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Question 369955: Please help me solve this word problem:
There is a 30-60-90 triangle with an area of 24 radical 3. What is the perimeter of this triangle, and what are the side lengths? (All in terms of X)
Thanks so much for the help.
Answer by mananth(12270) About Me  (Show Source):
You can put this solution on YOUR website!
in a 30-60-90 triangle the legs are x & xsqrt3
the hypotenuse = 2x
..
Area = !/2 * base * height
Area+=+1%2F2+%2A+x%2Ax%2Asqrt%283%29
+24+sqrt%283%29=+1%2F2%2Ax%2Ax%2Asqrt%283%29
multiply by 2
48sqrt%283%29=x%5E2%2Asqrt%283%29
divide by sqrt3
x^2= 48
x = 6.92
hypotenuse = 2*6.92= 13.84
second leg = x sqrt*(3)
=6.92*sqrt*(3)
= 11.98
..
perimeter = 11.98+6.92+13.84= 32.74

m.ananth@hotmail.ca