document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285786>Question 285786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is inscribed in a circle and the ratio between its width and length is 3:4.What is the ratio between the area of the rectangle and the area of the circle?\r<BR>\n" );
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document.write( "A. 12 : 25&#960;  B. 12 : 25  C. 48 : 25 &#960;  D. 25 : 48  E. None of these. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207245 by </B><A HREF=/tutors/aboutme.mpl?userid=Grinnell><B>Grinnell(63)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Grinnell><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the ratio between the width and the length is 3:4,<BR>\n" );
document.write( "then we represent the sides by 3x and 4x. (It does not matter about the actual length, we just know the ratio is 3 to 4.) Now the area is then going to be represented by 12x^2.<BR>\n" );
document.write( "Now we know the area of the rectangle is 12x^2 which will be in the numerator of our ratio answer.<BR>\n" );
document.write( "(12x^2 over something!)\r<BR>\n" );
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document.write( "Now the rectangle is inscribed in a circle, meaning that its vertices touch the circumfrence of the circle.<BR>\n" );
document.write( "It is now that we draw a picture!\r<BR>\n" );
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document.write( "Do you see that the diameter of the circle is the diagonal of the rectangle?<BR>\n" );
document.write( "What do we know about diagonals of rectangles? The point of intersection bisects the diagonals.<BR>\n" );
document.write( "But wait, do you also see the right triangle that we have formed? By the pythaoren (spelling, oops) theorem<BR>\n" );
document.write( "we know that a^2 plus b^2 equals c^2. (I assume you know this!)<BR>\n" );
document.write( "So, we have determined that the Diameter of the circle is the same as the Hypotenuse of the triangle formed. THIS IS 5X. <BR>\n" );
document.write( "Now the area of a circle is pi(r^2) r is 5x/2, then.\r<BR>\n" );
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document.write( "We just substitute...(5x/2)^2 (pi) =area of circle.<BR>\n" );
document.write( "this equals 25x^2 (pi)/2 (you do the math.)<BR>\n" );
document.write( "NOW THIS IS IN THE DENOMINATOR OF OUR RATIO ANSWER!!!\r<BR>\n" );
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document.write( "Write out the fraction:<BR>\n" );
document.write( "12x^2/25x^2 (pi)/4 Do the math we get...4/25x^2 (pi) TIMES 12x^2, the x^2 cancel out<BR>\n" );
document.write( "We are left with 48 over 25(pi)<BR>\n" );
document.write( "The answer is C. <BR>\n" );
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