document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620756>Question 620756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a square with diagonals of 10 cm long </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390390 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "We can solve this problem using the equation from the Pythagorean Theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. First, we'll find the side length of the square. Then we'll find the area of the square using the side length.<BR>\n" );
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document.write( "Draw a picture of a square. <BR>\n" );
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document.write( "Now draw in one of the diagonals from one corner to the opposite corner (for example, from the upper left corner to the lower right corner.)<BR>\n" );
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document.write( "Notice that you have two triangles inside the square. These are both right triangles because every corner of the square is a 90-degree angle.  Both triangles have the same shape, except that one is rotated upside down. The diagonal makes the hypotenuse of both triangles.<BR>\n" );
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document.write( "Let's have the variable s be the length of the sides of the square. <BR>\n" );
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document.write( "Look at one of the right triangles. Notice that both legs have a length of s, and the hypotenuse has a length of 10.<BR>\n" );
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document.write( "Use the the Pythagorean Equation. Substitute s for a and b, and 10 for c.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2Bs%5E2=10%5E2 ALIGN=MIDDLE  ALT=\"s%5E2%2Bs%5E2=10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for s.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%5E2=100 ALIGN=MIDDLE  ALT=\"2s%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=50 ALIGN=MIDDLE  ALT=\"s%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"s=sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we know that the side length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can use the formula for the area of a square.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=s%5E2 ALIGN=MIDDLE  ALT=\"A=s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for s in the formula.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28sqrt%2850%29%29%5E2 ALIGN=MIDDLE  ALT=\"A=%28sqrt%2850%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Taking the square root of a numer and squaring a number reciprocal operations--they undo each other (like adding and subtracting te same number.) This means that squaring the square root of 50 gives you 50.<BR>\n" );
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document.write( "The area of the square is 50 square centimeters.<BR>\n" );
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document.write( "Hope this helps, Feel free to email if you have questions about this.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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