The perimeter of an equilateral triangle is 1.25 times the circumference of a circle.
Quantity A
The area of the equilateral triangle
Quantity B
The area of the circle
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Go to it! My answer will appear in the comments.
By the way, sorry about the lack of posting last week. I think my sickness lingered on a bit longer than I had thought.
_
1 comment:
I'm going to give my vote to (B): the area of the circle is greater.
Why?
I worked it out this way:
Assume an equilateral triangle with side x.
Assume a circle with radius r.
So:
3x = 1.25(2πr)
3x = 2.5πr
r = 3x/(2.5π)
The area of the circle, then, is:
π•((3x/(2.5π))^2) =
(9x^2)/(6.25π)
The area of the equilateral triangle is:
((x^2)√3)/4
Let "Q" mean "greater than, less than, equal to (as yet undetermined)."
We need to compare areas:
[A(circle)] Q [A(triangle)]
[(9x^2)/(6.25π)] Q [((x^2)√3)/4]
Divide both sides of the Q-relation by x^2:
9/(6.25π) Q (√3)/4
Once we evaluate these expressions, we see the decimal approximations are:
.4583662 > .4330127
The area of the circle, then, is larger by a small margin.
QED.
By the way, this one would be hard to solve without a calculator, unless you happen to have memorized the decimal approximation for √3.
Post a Comment