document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353843>Question 353843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of a right triangle whose legs have lengths which differ by 7 meters and whose hypotenuse is 17 meters long. (Show your solution using Quadratic Equation) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252939 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the area of a right triangle whose legs have lengths which differ by 7 meters and whose hypotenuse is 17 meters long. (Show your solution using Quadratic Equation)<BR>\n" );
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document.write( "Once you see \"right triangle\" you can apply the Pythagorean theorem.<BR>\n" );
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document.write( "Let x = shortest leg<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x+7 = other leg<BR>\n" );
document.write( "17 = hypotenuse<BR>\n" );
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document.write( "x^2 + (x+7)^2 = 17^2\r<BR>\n" );
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document.write( "x^2 + (x+7)(x+7) = 17^2\r<BR>\n" );
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document.write( "x^2 + x^2+14x+49 = 289\r<BR>\n" );
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document.write( "2x^2+14x+49 = 289\r<BR>\n" );
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document.write( "2x^2+14x-240 = 0\r<BR>\n" );
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document.write( "x^2+7x-120 = 0 (your quadratic)\r<BR>\n" );
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document.write( "(x+15)(x-8) = 0\r<BR>\n" );
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document.write( "x = {-15, 8}\r<BR>\n" );
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document.write( "Throw out the negative solution leaving<BR>\n" );
document.write( "x = 8 meters (shortest leg)<BR>\n" );
document.write( "x+7 = 8+7= 15 meters (other leg)\r<BR>\n" );
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document.write( "Area is <BR>\n" );
document.write( "(1/2)bh<BR>\n" );
document.write( "(1/2)(8)(15)<BR>\n" );
document.write( "(4)(15)<BR>\n" );
document.write( "60 square meters </SPAN>\n" );
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