Question 1057484
An oval athletic field is the union of a square and semicircles at opposite ends, as shown in the figure below (http://www.webassign.net/jmodd7/8-1-034.gif).
 If the total area of the field is 1,300 square yards, find the dimensions of the square.
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Actually s also represents the diameter of the semi-circle; r = .5s
Two semi-circles = 1 circle
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Square area + circle area = 1300
{{{s^2 + pi*(.5s)^2}}} = 1300
{{{s^2 + pi*.25s^2}}} = 1300
Factor out s^2
{{{s^2(1+.25*pi)= 1300}}}
divide both sides by (1+.25pi0
{{{s^2 = 1300/(1+.25*pi)}}}
use your calc
s^2 = 728.129
s = {{{sqrt(728.129)}}}
s = 26.98 ~ 27 yards, one side of the square
:
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Check this on your calc; radius=13.5
27^2 + pi*13.5^2 = 1301.55, Because we rounded it off