document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394108>Question 394108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small commuter airline flies to 3 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279618 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small commuter airline flies to 3 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.<BR>\n" );
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document.write( "ABC is a right triangle<BR>\n" );
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document.write( "AB+BC+CA=1400 = perimeter of triangle<BR>\n" );
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document.write( "The longest side in a right triangle is the hypotenuse.<BR>\n" );
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document.write( "hypotenuse = 600<BR>\n" );
document.write( "if one leg is x then the other leg = 1400-600-x= 800-x<BR>\n" );
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document.write( "Use Pythagoras theorem<BR>\n" );
document.write( "leg1^2 +leg2^2=Hyp^2<BR>\n" );
document.write( "x^2+(1400-(600-x))^2=600^2\r<BR>\n" );
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document.write( "x^2+(800-x)^2=600^2<BR>\n" );
document.write( "x^2+640000-1600+x^2=360000<BR>\n" );
document.write( "2x^2-1600x+640000-360000=0<BR>\n" );
document.write( "2x^2-1600x+280000=0<BR>\n" );
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document.write( "x^2-800x+140,000=0<BR>\n" );
document.write( "slove using quadratic equation<BR>\n" );
document.write( "Find the roots of the equation by quadratic formula<BR>\n" );
document.write( "a=  1 , b = -800  , c = 140,000<BR>\n" );
document.write( "b^2-4ac= 80,000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1=%28800%2Bsqrt%2880000%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x1=%28800%2Bsqrt%2880000%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x= 541.42 miles<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2=%28800-sqrt%2880000%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x2=%28800-sqrt%2880000%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x2= 258.57 miles<BR>\n" );
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document.write( "m.ananth@hotmail.ca\r<BR>\n" );
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document.write( " </SPAN>\n" );
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