document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171698>Question 1171698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me out with this sum, i'm a little confused on how to do it...thank you in advance :))\r<BR>\n" );
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document.write( "A square has diagonals of length 10 cm. find the sides of the square.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796604 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=796604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = side length of the square<BR>\n" );
document.write( "Any square has all four sides the same length, so each side is x centimeters long.<BR>\n" );
document.write( "It doesn't make sense to have x be negative, so we'll say x > 0.\r<BR>\n" );
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document.write( "Draw a square with one diagonal only. We have the square divided into two congruent right triangles. Focus on one of those right triangles.\r<BR>\n" );
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document.write( "This right triangle has congruent legs (x cm each) and a hypotenuse that is 10 cm long.<BR>\n" );
document.write( "We'll let<BR>\n" );
document.write( "a = x<BR>\n" );
document.write( "b = x<BR>\n" );
document.write( "c = 10<BR>\n" );
document.write( "which will be plugged into the Pythagorean theorem to solve for x.\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "x^2 + x^2 = 10^2<BR>\n" );
document.write( "2x^2 = 100<BR>\n" );
document.write( "x^2 = 100/2<BR>\n" );
document.write( "x^2 = 50<BR>\n" );
document.write( "x = sqrt(50) .... applying the square root, keep in mind that x > 0<BR>\n" );
document.write( "x = sqrt(25*2)<BR>\n" );
document.write( "x = sqrt(25)*sqrt(2)<BR>\n" );
document.write( "x = 5*sqrt(2)\r<BR>\n" );
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document.write( "Each leg is exactly 5*sqrt(2) cm long\r<BR>\n" );
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document.write( "Therefore, each side of the square is 5*sqrt(2) cm long.\r<BR>\n" );
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document.write( "This is known as the exact answer because we don't have any decimal approximations going on. \r<BR>\n" );
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document.write( "Use of your calculator should lead to the rough approximation of<BR>\n" );
document.write( "5*sqrt(2) = 7.0710678<BR>\n" );
document.write( "Note that<BR>\n" );
document.write( "sqrt(50) = 7.0710678<BR>\n" );
document.write( "to help confirm that sqrt(50) = 5*sqrt(2)\r<BR>\n" );
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document.write( "----------------------------------------------\r<BR>\n" );
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document.write( "Exact Answer: 5*sqrt(2)   cm<BR>\n" );
document.write( "Approximate Answer: 7.0710678  cm<BR>\n" );
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