document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105794>Question 1105794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An artist is designing a logo for a business in the shape of a circle with an inscribed rectangle.the diameter of circle is 6.5 inches and the area of the rectangle is 15 square inches.Find the dimension of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720686 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both diagonals of the rectangle have the same length as the diameter of the circle<BR>\n" );
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document.write( "let l be the length of the rectangle and w be the width, then using the Pythagorean Theorem <BR>\n" );
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document.write( "l^2 + w^2 = 6.5^2 = 42.25<BR>\n" );
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document.write( "l = sqrt(42.25 - w^2)<BR>\n" );
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document.write( "we know the area(A) of the rectangle is 15 square inches and A = l * W, then<BR>\n" );
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document.write( "sqrt(42.25 - w^2) * w = 15<BR>\n" );
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document.write( "square both sides of =<BR>\n" );
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document.write( "(42.25 - w^2) * w^2 = 15<BR>\n" );
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document.write( "42.25w^2 - w^4 = 225<BR>\n" );
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document.write( "w^4 -42.25w^2 +225 = 0<BR>\n" );
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document.write( "let u = w^2, then<BR>\n" );
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document.write( "u^2 -42.25u + 225 = 0<BR>\n" );
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document.write( "(u-36) * (u-6.25) = 0<BR>\n" );
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document.write( "u = 36 or u = 6.25<BR>\n" );
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document.write( "since u = w^2, then w = sqrt(u)<BR>\n" );
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document.write( "w = 6 or 2.5<BR>\n" );
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document.write( "we have two possible rectangles<BR>\n" );
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document.write( "l = 15/6 = 2.5, w = 6<BR>\n" );
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document.write( "l = 15/2.5 = 6, w = 2.5<BR>\n" );
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