SOLUTION: A garden plot is in the shape of an equilateral triangle. The shortest distance from one corner to the opposite side if the area is 84 meters? Can you show me how you gonna solv it

Algebra ->  Angles -> SOLUTION: A garden plot is in the shape of an equilateral triangle. The shortest distance from one corner to the opposite side if the area is 84 meters? Can you show me how you gonna solv it      Log On


   

Question 1077985: A garden plot is in the shape of an equilateral triangle. The shortest distance from one corner to the opposite side if the area is 84 meters? Can you show me how you gonna solv it it. Pls. Thank you.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a line from a vertex to the opposite side.
By doing that, you make a pair of 30-60-90
triangles.
Let a side of the original equilateral triangle = +s+
So, now the sides of the 30-60-90 triangles are:
+s+
+s%2F2+
+sqrt%283%29%2F2%2As+ ( this one is the line that you drew )
The area of the equilateral triangle is:
+A+=+%281%2F2%29%2As%2A%28+sqrt%283%29%2F2%2As+%29+
+A+=+%281%2F4%29%2Asqrt%283%29%2As%5E2+
+84+=+%281%2F4%29%2Asqrt%283%29%2As%5E2+
+s%5E2+=+336%2Fsqrt%283%29+
+s%5E2+=+336%2Asqrt%283%29+%2F+3+
+s%5E2+=+112%2Asqrt%283%29+
+s+=+1.31607%2A10.583+
+s+=+13.928+
-------------------------
You want the line you drew, so
+sqrt%283%29%2F2%2As+=+%281.732%2F2%29%2A13.928+
+sqrt%283%29%2F2%2As+=+.866%2A13.928+
+sqrt%283%29%2F2%2As+=+12.062+ m answer
-----------------------------------
check:
+A+=+%281%2F2%29%2A13.928%2A12.062+
+A+=+83.9998+
this looks close enough
Definitely get a 2nd opinion on this!!!