document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878714>Question 878714</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a right triangle is 84 cm2. If four times length of one leg is 3 cm longer than the length of the hypotenuse, what are the measures of the three sides?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530239 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=530239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> GUESS AND CHECK STRATEGY:<BR>\n" );
document.write( "If you are not that deep into algebra and calculus, you are expected to try whole numbers for the lengths of the sides in centimeters.<BR>\n" );
document.write( "The area given is a clue. It is related to the product you get by multiplying the legs' lengths in centimeters.<BR>\n" );
document.write( "For a right triangle, you can take the length of one leg as the base, and the length of the other leg as the height, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area ALIGN=MIDDLE  ALT=\"area\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28leg%5B1%5D%29%28leg%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28leg%5B1%5D%29%28leg%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28leg%5B1%5D%29%28leg%5B2%5D%29%2F2=84 ALIGN=MIDDLE  ALT=\"%28leg%5B1%5D%29%28leg%5B2%5D%29%2F2=84\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28leg%5B1%5D%29%28leg%5B2%5D%29=84%2A2 ALIGN=MIDDLE  ALT=\"%28leg%5B1%5D%29%28leg%5B2%5D%29=84%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28leg%5B1%5D%29%28leg%5B2%5D%29=168 ALIGN=MIDDLE  ALT=\"%28leg%5B1%5D%29%28leg%5B2%5D%29=168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We look for pairs of factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=186 ALIGN=MIDDLE  ALT=\"186\"   DISABLED_style= \"max-width:90%; height:auto;\" > that could be the legs' lengths in centimeters.<BR>\n" );
document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=186=2%2A84=2%2A7%2A12=2%2A7%2A2%2A2%2A3=2%5E3%2A3%2A7 ALIGN=MIDDLE  ALT=\"186=2%2A84=2%2A7%2A12=2%2A7%2A2%2A2%2A3=2%5E3%2A3%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=186=7%2A%282%2A12%29=7%2A24 ALIGN=MIDDLE  ALT=\"186=7%2A%282%2A12%29=7%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" > sounds like a good possibility, because a hypotenuse so much longer that the \"one leg\" means that the other leg must also be much longer than the \"one leg\".<BR>\n" );
document.write( "In a right triangle with legs measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the hypotenuse measures<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%5E2%2B24%5E2%29=sqrt%2849%2B576%29=sqrt%28625%29=25 ALIGN=MIDDLE  ALT=\"sqrt%287%5E2%2B24%5E2%29=sqrt%2849%2B576%29=sqrt%28625%29=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Is \"four times\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"3 more than\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "YES. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A7=28=25%2B3 ALIGN=MIDDLE  ALT=\"4%2A7=28=25%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the lengths of the sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287cm%29 ALIGN=MIDDLE  ALT=\"highlight%287cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2824cm%29 ALIGN=MIDDLE  ALT=\"highlight%2824cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2825cm%29 ALIGN=MIDDLE  ALT=\"highlight%2825cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "Another way (no calculations involved, but your teacher may consider it cheating) would be to look up a list of Pythagorean triples. Those are sets of whole numbers that could be the lengths of the sides of a right triangle. (The squares of the first two numbers add up to the square of the third number).<BR>\n" );
document.write( "One of those triples is 7 24 25, and it is the only one where 7 appears as a factor, and the two first numbers are factors of 186.<BR>\n" );
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document.write( "NOT GUESS AND CHECK?<BR>\n" );
document.write( "Then you may have to start writing equations and may loose sight of the triangle issue. </SPAN>\n" );
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