document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254063>Question 254063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) A farmer wishes to put a diagonal brace on his gate. How long should the brace be if the gate is rectangular, 12 by 5 ft? \r<BR>\n" );
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document.write( "2.) A trunk is 4 x 3 x 2 ft. What is the longest rod that this truck can contain?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186382 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=186382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both questions rely on the Pythagorean formula:  c^2 = a^2 + b^2.<BR>\n" );
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document.write( "The diagonal brace on the gate would be the hypotenuse of a right triangle with a=12 and b=5.<BR>\n" );
document.write( "a^2 = 144<BR>\n" );
document.write( "b^2 = 25<BR>\n" );
document.write( "so<BR>\n" );
document.write( "c^2 = 169<BR>\n" );
document.write( "By inspection we see that is a perfect square:  sqrt(169) = 13.<BR>\n" );
document.write( "That means the brace must be 13 ft.<BR>\n" );
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document.write( "The longest rod that can fit in a trunk will fit in three dimensions, for example, from the lower left front corner to the upper right back corner.<BR>\n" );
document.write( "The height of the triangle will be one of known dimensions.<BR>\n" );
document.write( "We are told 4x3x2, so we have to assume these are length by width by height.<BR>\n" );
document.write( "a^2 = height^2 = 2^2 = 4<BR>\n" );
document.write( "The other leg of the triangle the rod defines will be the diagonal of the base of the trunk.<BR>\n" );
document.write( "The base of the trunk is a rectangle that is 4x3, so the diagonal will be 5.<BR>\n" );
document.write( "b^2 = base^2 = 5^2 = 25<BR>\n" );
document.write( "c^2 = 4 + 25 = 29<BR>\n" );
document.write( "c = sqrt(29) = 5.385 </SPAN>\n" );
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