document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113494>Question 1113494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A canvas camping tent is to be constructed in the shape of a pyramid with a square base. A pole of height h = 12 feet will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 864 ft^2. </SPAN>\n" );
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document.write( "The base is a square of side length x; its area is x^2.<br><BR>\n" );
document.write( "The sides of the tent are four congruent triangles with base x.<BR>\n" );
document.write( "The altitude of each triangle is the slant height of the pyramid.<BR>\n" );
document.write( "With the square base of side length x and a center pole of 12, the slant height is the hypotenuse of a right triangle with legs x/2 and 12.<br><BR>\n" );
document.write( "So the area of each triangular side of the tent is one-half base times height:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28x%29%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28x%29%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total surface area of the four sides and bottom of the tent is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This total surface area is to be 864:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29+=+864 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29+=+864\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29+=+864-x%5E2 ALIGN=MIDDLE  ALT=\"2x%28sqrt%28%28x%2F2%29%5E2%2B12%5E2%29%29+=+864-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%28x%5E2%2F4%2B144%29+=+746496-1728x%5E2%2Bx%5E4 ALIGN=MIDDLE  ALT=\"4x%5E2%28x%5E2%2F4%2B144%29+=+746496-1728x%5E2%2Bx%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(Looks ugly -- but the x^4 terms will cancel, leaving a simple quadratic equation...)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B576x%5E2+=+746496-1728x%5E2%2Bx%5E4 ALIGN=MIDDLE  ALT=\"x%5E4%2B576x%5E2+=+746496-1728x%5E2%2Bx%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304x%5E2+=+746496 ALIGN=MIDDLE  ALT=\"2304x%5E2+=+746496\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+324 ALIGN=MIDDLE  ALT=\"x%5E2+=+324\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18 ALIGN=MIDDLE  ALT=\"x+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer: The side length of the tent is 18 feet.<br><BR>\n" );
document.write( "(by the way... I don't think this is a CAMPING tent!!) </SPAN>\n" );
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