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) (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
= 60
r^2 =
r =
r = 4.37 is the radius
:
The triangle (s=side)
*s*h = 60
Find the height of the triangle in terms of s
h =
h =
h =
Area of the triangle
*s*h = 60
s * h = 120; mult both sides by 2
Replace h with
s * = 120
Square both sides
s^2 * .75s^2 = 14400
.75s^4 = 14400
s^4 =
s^4 = 19200
Find the 4th root of both sides
s = 19200^(1/4)
s = 11.77 is the side of triangle
:
~ 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.
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