SOLUTION: if the area of a circle is equal to the area of an equilateral triangle , then the ratio of the side of the triangle to the radius of the circle is closest to which number ? a

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Question 313783: if the area of a circle is equal to the area of an equilateral triangle , then the ratio of the side of the triangle to the radius of the circle is closest to which number ?
a 3 b 4 c 5 d 6 e 7
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
if the area of a circle is equal to the area of an equilateral triangle,
then the ratio of the side of the triangle to the radius of the circle is closest to which number?
:
Choose a value for the area; A = 60
pi%2Ar%5E2 = 60
r^2 = 60%2Fpi
r = sqrt%2819.1%29
r = 4.37 is the radius
:
The triangle (s=side)
1%2F2*s*h = 60
Find the height of the triangle in terms of s
h = sqrt%28s%5E2+-+%28.5s%29%5E2%29
h = sqrt%28s%5E2+-+.25s%5E2%29
h = sqrt%28.75s%5E2%29
Area of the triangle
1%2F2*s*h = 60
s * h = 120; mult both sides by 2
Replace h with sqrt%28.75s%5E2%29
s * sqrt%28.75s%5E2%29 = 120
Square both sides
s^2 * .75s^2 = 14400
.75s^4 = 14400
s^4 = 14400%2F.75
s^4 = 19200
Find the 4th root of both sides
s = 19200^(1/4)
s = 11.77 is the side of triangle
:
11.77%2F4.37 ~ 2.7, closest to 3
:
:
seems like there should be a more elegant way to do this, but I can't come up with it.