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Mathematics
OpenStudy (anonymous):

A wire of length 2p is bent to form a circle, a triangle , a rectangle and a polygon. State which figure has the greatest area.

OpenStudy (bahrom7893):

I think it's always supposed to be a circle..

OpenStudy (anonymous):

how pls tell

OpenStudy (bahrom7893):

hmm well use maximization... Did you take calculus before?

OpenStudy (anonymous):

NO BUT THE BOOK IS SAYING THE ANSWER AS RECTANGLE PLS HEP

OpenStudy (bahrom7893):

okay so let me try optimizing..

OpenStudy (bahrom7893):

it is definitely not a polygon, for the rest, find the dimensions and solve for the area..

OpenStudy (anonymous):

I WAS TRYING BUT NOT SUCCESS IN IT PLS SOLVE U I M HAVING PROLBEMS

OpenStudy (bahrom7893):

when is this due? because I gtg to bed..

OpenStudy (anonymous):

OK BYE

OpenStudy (bahrom7893):

Okay ill finish this, i was asking a proper question no need to be rude. Anyway: 1) try a circle, if you make a circle out of the wire, then circumference will equal to the length of the wire, so: C = 2 pi * r = 2p 2 pi * r = 2p pi * r = p r = p / pi

OpenStudy (bahrom7893):

Now find the area of that circle, which will be A = pi r^2 = pi * ( p / pi ) ^2 = pi^2 / p A(circle) = pi^2 / p

OpenStudy (bahrom7893):

is the triangle equilateral?

OpenStudy (anonymous):

The more perfect the figure, the larger the area. That is as the polygon with n sides where n goes to infinity, it will approach the area of the circle. But the circle is a perfect figure and hence has the largest area. Just use a simple example to show this. For example, let the perimeter=12, so the square will have side 3 and area 9 square units. Since a square is a perfect quadrilateral, it will have a larger area than a rectangle (unless the rectangle is a square). This comes from the fact that since you are multiplying two different divisors of the same number, the largest number is always found by using the same number twice (the square root, just like the area of a square). For example, use a rectangle having sides 2,2,4,4 instead with the same perimeter of 12. The area will be 8, which is less than 9. For an equilateral triangle, its area (being a perfect figure, but with fewer sides than a square will be smaller. In the case of a polygon, as the number of sides gets larger, its area will approach that of the circle but it will still be less than that of the circle. Think of the polygon as being drawn inside the circle.

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