document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073352>Question 1073352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4 semicircle and 4 quadrant each of radius 7cm were cut off from a rectangular cardboard if perimeter 128cm.Find the perimeter of the cut cardboard. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688187 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without more detail, some assumptions need to be made.<BR>\n" );
document.write( " <BR>\n" );
document.write( "1) For starters, we need a conveniently shaped rectangle,<BR>\n" );
document.write( "with enough usable surface area, such as a 16 cm by 48 cm rectangle.<BR>\n" );
document.write( "Not all rectangles with a perimeter of 128 cm will yield<BR>\n" );
document.write( "4 semicircles and 4 quadrants each of radius 7cm.<BR>\n" );
document.write( "For example, a rectangle of with 8 cm and length 56 cm has a perimeter of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%285cm%2B56cm%29=2%2A64cm=128cm ALIGN=MIDDLE  ALT=\"2%285cm%2B56cm%29=2%2A64cm=128cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but it cannot yield 4 semicircles and 4 quadrants each of radius 7cm,<BR>\n" );
document.write( "not even reshaping the cutouts to make circular sectors out of the wasted cutout pieces.<BR>\n" );
document.write( "That rectangle has an area of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2856cm%29%288cm%29=488cm%5E2 ALIGN=MIDDLE  ALT=\"%2856cm%29%288cm%29=488cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "while 4 semicircles and 4 quadrants each of radius 7cm<BR>\n" );
document.write( "add to a larger total surface area.<BR>\n" );
document.write( "They have the same total area as the 3 circles of radius 7cm they would form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Api%2A%287cm%29%5E2=about+461.8cm%5E2 ALIGN=MIDDLE  ALT=\"3%2Api%2A%287cm%29%5E2=about+461.8cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "2) Then, there is the issue of where to cut from.<BR>\n" );
document.write( "One practical way, would be to cut the quadrants from the corners,<BR>\n" );
document.write( "and the semicircles along the long edges of the rectangle,<BR>\n" );
document.write( "with the straight sector edges along the  sides of the rectangle,<BR>\n" );
document.write( "like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28520%2C200%2C-2%2C50%2C-2%2C18%2C%0D%0Ared%28rectangle%280%2C0%2C48%2C16%29%29%2C%0D%0Aarc%280%2C0%2C14%2C14%2C-90%2C0%29%2Carc%280%2C16%2C14%2C14%2C0%2C90%29%2C%0D%0Aarc%2848%2C0%2C14%2C14%2C180%2C270%29%2Carc%2848%2C16%2C14%2C14%2C90%2C180%29%2C%0D%0Aarc%2816%2C0%2C14%2C14%2C180%2C360%29%2Carc%2816%2C16%2C14%2C14%2C0%2C180%29%2C%0D%0Aarc%2832%2C0%2C14%2C14%2C180%2C360%29%2Carc%2832%2C16%2C14%2C14%2C0%2C180%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "With the assumptions above about<BR>\n" );
document.write( "1) the shape of the rectangle, and<BR>\n" );
document.write( "2) the way the circular sectors  were cut off,<BR>\n" );
document.write( "we are left with a piece that has for perimeter<BR>\n" );
document.write( "some segments of the rectangle's straight edges, and<BR>\n" );
document.write( "the curved edges of 3 circles.<BR>\n" );
document.write( "The curved edges of 3 circles add up to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%282pi%287cm%29%29=pi%2A42cm=about131.95cm ALIGN=MIDDLE  ALT=\"3%282pi%287cm%29%29=pi%2A42cm=about131.95cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For each circular sector piece cut off,<BR>\n" );
document.write( "the removed segment(s) of the rectangle's edges were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A7cm=14cm ALIGN=MIDDLE  ALT=\"2%2A7cm=14cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So what's left as straight segments of the rectangle's original perimeter is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128cm-8%2A14cm=128cm-112cm=16cm ALIGN=MIDDLE  ALT=\"128cm-8%2A14cm=128cm-112cm=16cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the straight plus curved parts of the perimeter of the<BR>\n" );
document.write( "piece leftoever of the rectangle is approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16cm%2B131.95cm=highlight%28147.95cm%29 ALIGN=MIDDLE  ALT=\"16cm%2B131.95cm=highlight%28147.95cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If an exact expression is required, it would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16cm%2Bpi%2A42cm=highlight%2816%2B42pi%29cm ALIGN=MIDDLE  ALT=\"16cm%2Bpi%2A42cm=highlight%2816%2B42pi%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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