document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516460>Question 516460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem. \"A piece of property is in the shape of a right triangle. The longer leg is 20 meters longer than than twice the length of the shorter leg. The hypotenuse is 10 meters longer than the length of the longer leg. Find the lengths of the sides of the triangular lot.\" I made the longer side a, the shorter side b, and the hypotenuse c. I figured out: a=2b+20 and c=a+10. Then combined them to get c=2b+20+10, then c=2b+30, and that's where I'm stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344430 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"A piece of property is in the shape of a right triangle.<BR>\n" );
document.write( " The longer leg is 20 meters longer than than twice the length of the shorter leg.<BR>\n" );
document.write( " The hypotenuse is 10 meters longer than the length of the longer leg.<BR>\n" );
document.write( " Find the lengths of the sides of the triangular lot.\"<BR>\n" );
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document.write( "Using your equations<BR>\n" );
document.write( "Longer leg<BR>\n" );
document.write( "a = 2b+20<BR>\n" );
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document.write( "Hypot<BR>\n" );
document.write( "c = a + 10<BR>\n" );
document.write( "c = 2b + 30<BR>\n" );
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document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "Replacing a and c<BR>\n" );
document.write( "(2b+20)^2 + b^2 = (2b+30)^2<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "4b^2 + 80b + 400 + b^2 = 4b^2 + 120b + 900<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "4b^2 + b^2 - 4b^2 + 80b - 120b + 400 -900 = 0<BR>\n" );
document.write( "b^2 - 40b - 500 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(b-50)(b+10) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "b = 50 is the shorter leg<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 2(50) + 20<BR>\n" );
document.write( "a = 120 is the longer leg<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 2(50) + 30<BR>\n" );
document.write( "c = 130 is the hypotenuse<BR>\n" );
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document.write( "Check on a calc, enter: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%5E2+%2B+120%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%5E2+%2B+120%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  results = 130 confirms our solutions </SPAN>\n" );
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