document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115244>Question 115244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a square is 20 centimeters.  Find the length of a diagonal. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83828 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=83828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sketch a square. Label each of its sides with 20. Then sketch in a diagonal. You will see<BR>\n" );
document.write( "that the diagonal divides the square into two right triangles. Each of these triangles<BR>\n" );
document.write( "has legs that are both 20 units long and the diagonal of the square is the hypotenuse<BR>\n" );
document.write( "of the triangles.<BR>\n" );
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document.write( "This problem can be solved by using the Pythagorean theorem. (The Pythagorean theorem<BR>\n" );
document.write( "applies only to right triangles.) The Pythagorean theorem says that the sum of the squares<BR>\n" );
document.write( "of the two legs of a right triangle equals the square of the hypotenuse. In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
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document.write( "A^2 + B^2 = H^2<BR>\n" );
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document.write( "where A and B are the legs of the triangle.  In this problem both A and B are 20. So<BR>\n" );
document.write( "replace them with 20 and you get:<BR>\n" );
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document.write( "20^2 + 20^2 = H^2<BR>\n" );
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document.write( "But 20^2 is 400. Substitute that into the equation and you get:<BR>\n" );
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document.write( "400 + 400 = H^2<BR>\n" );
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document.write( "Do the addition on the left side and the equation becomes:<BR>\n" );
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document.write( "800 = H^2<BR>\n" );
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document.write( "Transpose this equation (switch sides):<BR>\n" );
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document.write( "H^2 = 800<BR>\n" );
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document.write( "Solve for H by taking the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+sqrt%28800%29+ ALIGN=MIDDLE  ALT=\"H+=+sqrt%28800%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then apply some rules of square roots to simplify the answer. The square root of a number <BR>\n" );
document.write( "equals the square root of the product of its factors. So we can write:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28800%29+=+sqrt%28400%2A2%29 ALIGN=MIDDLE  ALT=\"sqrt%28800%29+=+sqrt%28400%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then the square root of a product of terms is equal to the product of the square roots of <BR>\n" );
document.write( "each of the terms. So, we can further say:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28400%2A2%29+=+sqrt%28400%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%28400%2A2%29+=+sqrt%28400%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But the square root of 400 is 20. So this further simplifies to:<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28400%2A2%29+=+sqrt%28400%29%2Asqrt%282%29+=+20%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%28400%2A2%29+=+sqrt%28400%29%2Asqrt%282%29+=+20%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer to this problem is that the diagonal H of the square is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+20%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"H+=+20%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > centimeters<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
document.write( ". </SPAN>\n" );
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