document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935727>Question 935727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A single piece of rectangular cardboard can be folded around a 5” by 7” photo and taped along the seams to create a protective cover suitable for mailing. If the cardboard is folded as shown with no gap or overlap, find the dimensions of the original cardboard. Round to the nearest hundredth. (HINT: Use Theorem 6.9 states: In a right triangle, the altitude to the hypotenuse is the mean proportional between the two segments formed by the altitude on the hypotenuse.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i1081.photobucket.com/albums/j358/Reina_Lopez/prob41_zps6657d54c.png\"> </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569016 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = small right triangle with 5\" hypotenuse<BR>\n" );
document.write( "B = large right triangle with 7\" hypotenuse<BR>\n" );
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document.write( "x = short side of A:<BR>\n" );
document.write( "y = long side of A:<BR>\n" );
document.write( "z = short side of B:<BR>\n" );
document.write( "w = long side of B:<BR>\n" );
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document.write( "triangles A and B together form a third triangle similar to A and similar to B, but larger than A, lets call this third triangle C<BR>\n" );
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document.write( "u = hypotenuse of C:<BR>\n" );
document.write( "u = sqrt( 5*5 + 7*7 )<BR>\n" );
document.write( "u = 8.60232526704<BR>\n" );
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document.write( "use the proportionality of similar triangles A and C:<BR>\n" );
document.write( "(short side of A)/(hypotenuse of A) = (short side of C)/(hypotenuse of C)<BR>\n" );
document.write( "x/5 = 5/u<BR>\n" );
document.write( "x/5 = 5/u<BR>\n" );
document.write( "x = 5*5/u<BR>\n" );
document.write( "x = 5*5/8.60232526704<BR>\n" );
document.write( "x = 2.9061909686<BR>\n" );
document.write( "---<BR>\n" );
document.write( "use the proportionality of similar triangles A and C:<BR>\n" );
document.write( "(long side of A)/(hypotenuse of A) = (long side of C)/(hypotenuse of C)<BR>\n" );
document.write( "y/5 = 7/u<BR>\n" );
document.write( "y = 5*7/u<BR>\n" );
document.write( "y = 5*7/8.60232526704<BR>\n" );
document.write( "y = 4.06866735603<BR>\n" );
document.write( "---<BR>\n" );
document.write( "use the proportionality of similar triangles B and C:<BR>\n" );
document.write( "(short side of B)/(hypotenuse of B) = (short side of C)/(hypotenuse of C)<BR>\n" );
document.write( "z/7 = 5/u<BR>\n" );
document.write( "z = 7*5/u<BR>\n" );
document.write( "z = 7*5/8.60232526704<BR>\n" );
document.write( "z = 4.06866735603<BR>\n" );
document.write( "---<BR>\n" );
document.write( "use the proportionality of similar triangles B and C:<BR>\n" );
document.write( "(long side of B)/(hypotenuse of B) = (long side of C)/(hypotenuse of C)<BR>\n" );
document.write( "w/7 = 7/u<BR>\n" );
document.write( "w = 7*7/u<BR>\n" );
document.write( "w = 7*7/8.60232526704<BR>\n" );
document.write( "w = 5.69613429845<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the folding corners of the cardboard are just similar copies of triangles A and B:<BR>\n" );
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document.write( "dimensions of the cardboard:<BR>\n" );
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document.write( "length of top-left edge = length of bottom-right edge = y + z<BR>\n" );
document.write( "y + z = 4.06866735603 + 4.06866735603<BR>\n" );
document.write( "y + z = 8.13733471206<BR>\n" );
document.write( "---<BR>\n" );
document.write( "length of top-right edge = length of bottom-left edge = x + w<BR>\n" );
document.write( "x + w = 2.9061909686 + 5.69613429845<BR>\n" );
document.write( "x + w = 8.60232526705<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "L = 8.60 inches<BR>\n" );
document.write( "W = 8.14 inches<BR>\n" );
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