document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039482>Question 1039482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a right triangle is 105m^2. The hypotenuse has length square root 421m. What are the lengths of the legs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654231 by </B><A HREF=/tutors/aboutme.mpl?userid=Aldorozos><B>Aldorozos(172)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Aldorozos><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's assume one side as x and the other side as y. We have to find the values of x and y\r<BR>\n" );
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document.write( "We have two equations and two unknowns. <BR>\n" );
document.write( "The first equation is x*y *1/2 = 105m^2 = area\r<BR>\n" );
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document.write( "The second equation is from Pythagorean theorem\r<BR>\n" );
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document.write( "x^2 + y^2 = (Sqrt 421m)^2 = 421m\r<BR>\n" );
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document.write( "Now we have both equations<BR>\n" );
document.write( "x*y *1/2 = 105m^2<BR>\n" );
document.write( "x^2 + y^2  = 421m\r<BR>\n" );
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document.write( "We can calculate the value of y from the first equation in terms of x and replace the y of the second equation with what we found for x from the first equation.\r<BR>\n" );
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document.write( "x*y *1/2 = 105m^2 therefore x*y = 2(105m^2) and then y = 210m^2/x now we can replace y in the second equation with 210m^2/x\r<BR>\n" );
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document.write( "x^2 + (210m^2/x)^2 = (421m)^2\r<BR>\n" );
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document.write( "x^2 + (210m^2)^2/x^2 = (421m)^2\r<BR>\n" );
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document.write( "Lets multiply both sides of the equation by x^2 to get rid of x^2 in the denomination\r<BR>\n" );
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document.write( "x^4 + (210m^2)^2 = (421m)^2 *x^2\r<BR>\n" );
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document.write( "x^4 - (421m)^2 *x^2 + (210m^2)^2 = 0\r<BR>\n" );
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document.write( "This is similar to a quadratic equation Lets assume x^2 = z Then we can rewrite the equation \r<BR>\n" );
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document.write( "z^2 - (421m)^2 *z + (210m^2)^2 = 0 This is a quadratic equation If we solve this quadratic equation we find z in terms of m. For example z = 9m^2 (please note 9m^2 is a hypothetical example. To get the accurate number we have to solve the quadratic equation\r<BR>\n" );
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document.write( "If z = 9m^2 then x^2 = 9m^2 and therefore x = 3m Now that we found x we can use one of the equations to find y.<BR>\n" );
document.write( "The easiest is to use x.y/2 = 105m^2 we know x = 3m Therefore 3m.y/2 = 105m^2<BR>\n" );
document.write( "and this allows us to calculate y in terms of m. We have to multiply both sides by two and then divide both sides by three. To calculate the exact values of x and y of course we have to solve the quadratic equation:<BR>\n" );
document.write( "z^2 - (421m)^2 *z + (210m^2)^2 = 0\r<BR>\n" );
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document.write( " </SPAN>\n" );
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