SOLUTION: Please help me to solve this: The largest area of an equilateral triangle which can be formed by a given length of a wire is 484√3sq.cm.If the same wire is bent twice,first t

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Question 986300: Please help me to solve this: The largest area of an equilateral triangle which can be formed by a given length of a wire is 484√3sq.cm.If the same wire is bent twice,first to form a circle and then a square; find the ratio between there area
Answer: 14:11
This Questions is from circumference and area of a circle
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the total length of wire.
The area of an equilateral triangle of given length s is,
A%5Beq%5D=%28sqrt%283%29%2F4%29s%5E2=484sqrt%283%29
s%5E2=1936
s=44
Since there are three sides, the total length of wire is 3s,
L=3s=3%28144%29=132
For a square,
L=4s
and
A%5Bs%5D=s%5E2
A%5Bs%5D=L%5E2%2F16=132%5E2%2F16=1089
and for a circle,
L=C=2pi%2AR
R=L%2F%282pi%29
R=132%2F%282pi%29=66%2Fpi
and
A%5Bc%5D=pi%2AR%5E2
A%5Bc%5D=pi%2A%2866%2Fpi%29%5E2
A%5Bc%5D=4356%2Fpi
So,
A%5Bc%5D%2FA%5Bs%5D=%284356%29%2Fpi%2F%281089%29
A%5Bc%5D%2FA%5Bs%5D=4%2Fpi
Not exactly 14%2F11 but very close.