document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947539>Question 947539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.please help me to solve this problem abcd is quadrilateral prove that (ab+bc+cd+da)>(av+bd)<BR>\n" );
document.write( "2.find the length of hypotenuse of right triangle,the other two sides are<BR>\n" );
document.write( "9 cm,12 cm <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578200 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Points A, B, C, and D are the vertices of the quadrilateral<BR>\n" );
document.write( "(I write them as capital letters, because points are usually named that way),<BR>\n" );
document.write( "but what point is V? Or did you mean B?<BR>\n" );
document.write( "If ABCD is quadrilateral,<BR>\n" );
document.write( "BD is a diagonal, and of course<BR>\n" );
document.write( "BD < BC + CD<BR>\n" );
document.write( "That is because a straight line is the shorter distance between two points,<BR>\n" );
document.write( "or because the length of a side of any triangle (such as side BD of triangle BCD)<BR>\n" );
document.write( "is less than the sum of the lengths of the other two sides (sides BC and CD).<BR>\n" );
document.write( "Those are two ways of saying the same thing.<BR>\n" );
document.write( "So, since BD < BC + CD,<BR>\n" );
document.write( "then, BD < BC + CD ---> AB + BD < AB + BC + CD  < AB + BC + CD +DA<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. What your teacher expects is that you use a calculator and the Pythagorean theorem,<BR>\n" );
document.write( "that says that for a right triangle,<BR>\n" );
document.write( "the square of the length of the hypotenuse is<BR>\n" );
document.write( "the sum of the squares of the lengths of the other two sides (called legs).<BR>\n" );
document.write( "In your case, with the lengths in cm,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse%5E2=9%5E2%2B12%5E2 ALIGN=MIDDLE  ALT=\"hypotenuse%5E2=9%5E2%2B12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse%5E2=81%2B144 ALIGN=MIDDLE  ALT=\"hypotenuse%5E2=81%2B144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse%5E2=225 ALIGN=MIDDLE  ALT=\"hypotenuse%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse=sqrt%28225%29 ALIGN=MIDDLE  ALT=\"hypotenuse=sqrt%28225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now (unless you remember squares of small numbers as I do),<BR>\n" );
document.write( "you use a calculator to find that square root, and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse=highlight%2815%29 ALIGN=MIDDLE  ALT=\"hypotenuse=highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the length of the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815cm%29 ALIGN=MIDDLE  ALT=\"highlight%2815cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "However, if you do not have to show your work,<BR>\n" );
document.write( "and especially if you need to solve the problem quickly for a timed test,<BR>\n" );
document.write( "there is a faster way to the answer:<BR>\n" );
document.write( "A very popular Pythagorean triple is (3,4,5),<BR>\n" );
document.write( "meaning that a right triangle with legs measuring 3, and 4,<BR>\n" );
document.write( "has a hypotenuse measuring 5 (measured in whatever units you choose).<BR>\n" );
document.write( "That triangle can be scaled up, by multiplying all measurements by the same number.<BR>\n" );
document.write( "Multiplying times 2, we get the triple (6,8,10);<BR>\n" );
document.write( "multiplying times 3, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28%22 ALIGN=MIDDLE  ALT=\"%22%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%289%29 ALIGN=MIDDLE  ALT=\"red%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%2812%29 ALIGN=MIDDLE  ALT=\"green%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815%29 ALIGN=MIDDLE  ALT=\"highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "So, I do not need to to do much calculation to know that in a right triangle,<BR>\n" );
document.write( "if the lengths of the legs are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%289%29 ALIGN=MIDDLE  ALT=\"red%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%2812%29 ALIGN=MIDDLE  ALT=\"green%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm ,<BR>\n" );
document.write( "the length of hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815+cm%29 ALIGN=MIDDLE  ALT=\"highlight%2815+cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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