SOLUTION: What is the length of a side of an equilateral triangle whose altitude has a length of 20? My answer is about 23, but I'm not sure if it is correct. Also, is it possible to put th

Algebra ->  Triangles -> SOLUTION: What is the length of a side of an equilateral triangle whose altitude has a length of 20? My answer is about 23, but I'm not sure if it is correct. Also, is it possible to put th      Log On


   

Question 580595: What is the length of a side of an equilateral triangle whose altitude has a length of 20?
My answer is about 23, but I'm not sure if it is correct. Also, is it possible to put the answer is simplest radical form?
Please explain. Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
With the altitude drawn, you have two 30-60-90
triangles. The altitude is opposite the
60 degree angle.
The ratio of the side of the equilateral to
the altitude is +2%2Fsqrt%283%29+
Call the side s
+2%2Fsqrt%283%29+=+s%2F20+
+2%2A20+=+s%2Asqrt%283%29+
+s+=+40%2Fsqrt%283%29+
+s+=+%2840%2Fsqrt%283%29%29%2A%28+sqrt%283%29%2Fsqrt%283%29+%29+
+s+=+%28+40%2Asqrt%283%29+%29%2F3+
and
+s+=+%2840%2A1.732%29%2F3+
+s+=+23.09+