document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254766>Question 254766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small commuter airline flies to three cities whose locations form the vertices of a right triangle.. The total flight distance (from city A to City B to city C and back to city A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. Find the other two distances between cities.\r<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 #187071 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=187071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small commuter airline flies to three cities whose locations form the vertices of a right triangle.. The total flight distance (from city A to City B to city C and back to city A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. Find the other two distances between cities. \r<BR>\n" );
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document.write( "Let's suppose the longest side of the right triangle is AC. Then AC = 600 miles. Since the perimeter of the triangle is 1400, the sum of the other sides, AB and BC is 1400-600 = 800. \r<BR>\n" );
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document.write( "Since AB + BC = 800, AB = 800 - BC.\r<BR>\n" );
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document.write( "By the Pythagorean Theorem we have:\r<BR>\n" );
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document.write( "AC^2 = AB^2 + BC^2 so\r<BR>\n" );
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document.write( "600^2 = (800-BC)^2 + BC^2\r<BR>\n" );
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document.write( "3600 = 6400 - 1600*BC + BC^2 + BC^2<BR>\n" );
document.write( "2*BC^2 - 1600*BC + 2800 = 0  <BR>\n" );
document.write( "BC^2 - 800*BC + 1400 = 0\r<BR>\n" );
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document.write( "Solve this quadratic equation for BC then calculate AC = 800-BC.<BR>\n" );
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