document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196592>Question 1196592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two straight wires are attached at a point 24 feet above the base of a vertical pole standing on level ground. One wire is 5 feet longer than the other and reaches a point on the ground 11 feet farther from the base. Find the length of each. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829495 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The given information defines a picture consisting of two right triangles sharing one leg of length 24 and with the other legs of lengths x and x+11; and the hypotenuse of the larger triangle is 5 longer than the hypotenuse of the smaller triangle.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2%2C20%2C-2%2C30%0D%0A%2Cline%280%2C0%2C20%2C0%29%2Cline%280%2C0%2C0%2C26%29%2Cline%280%2C24%2C7%2C0%29%2Cline%280%2C24%2C18%2C0%29%0D%0A%2Clocate%283%2C0%2Cx%29%2Clocate%2810%2C0%2C11%29%2Clocate%28.5%2C12%2C24%29%2Clocate%280%2C0%2CO%29%2Clocate%28.5%2C25%2CA%29%2Clocate%287%2C0%2CB%29%2Clocate%2818%2C0%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The requirement is that AC is 5 longer than AB:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%5E2%2B%28x%2B11%29%5E2%29=sqrt%2824%5E2%2Bx%5E2%29%2B5 ALIGN=MIDDLE  ALT=\"sqrt%2824%5E2%2B%28x%2B11%29%5E2%29=sqrt%2824%5E2%2Bx%5E2%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving that equation algebraically is ugly; using a graphing calculator would be much easier.<br><BR>\n" );
document.write( "But since the numbers in the problem are whole numbers, we can guess the solution knowing something about Pythagorean Triples.<br><BR>\n" );
document.write( "A relatively well-known Pythagorean Triple is 7-24-25. So if x is 7 and AB is 25, then x+11 is 18 and AC is 30; and 18-24-30 is also a Pythagorean Triple.<br><BR>\n" );
document.write( "So, whether you solve the problem algebraically, or using a graphing calculator, or by logical trial and error, the lengths of the two wires are 25 feet and 30 feet.<br><BR>\n" );
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