document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047238>Question 1047238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good Morning! Hopefully this fits into the category of Proportions.  We have a real situation where we're hoping to fit a heavy object into a given space.  Because of smaller solid barriers at the entry of the space the object (a microwave oven) must be placed into the space length-wise (rather than width-wise). The question is whether or not, once into the space, the object can be twisted 90 degrees into it's desired orientation.  The height of both the space & object along with the depth of the space do not play into consideration of the problem.     <BR>\n" );
document.write( "Space: 23.5 inches wide<BR>\n" );
document.write( "Object: 21.9 inches wide & 17.35 inches deep <BR>\n" );
document.write( "Thank you for tackling this query,  John        </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662766 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=662766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I cannot imagine how this can be real, or how the depth of the space would not play into consideration.<BR>\n" );
document.write( "Maybe you are trying to store that microwave on a shelf at the back of a narrow walk-in closet.<BR>\n" );
document.write( "but here is how I interpret the question.<BR>\n" );
document.write( "From above, the entry space, and the space where the object will be turned around look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-42%2C14%2C-14%2C14%2C%0D%0Aline%28-36%2C-11.75%2C-36%2C11.75%29%2C%0D%0Aline%28-36%2C-11.75%2C0%2C-11.75%29%2C%0D%0Aline%28-36%2C11.75%2C0%2C11.75%29%2C%0D%0Alocate%28-39.5%2C2.5%2C23.5%29%2Clocate%28-41%2C0.5%2Cinches%29%2C%0D%0Aline%280%2C-11.75%2C0%2C-10%29%2C%0D%0Aline%280%2C11.75%2C0%2C10%29%2C%0D%0Aline%280%2C-10%2C2%2C-10%29%2C%0D%0Aline%280%2C10%2C2%2C10%29%2C%0D%0Alocate%28-25%2C-10.25%2Cdepth%3Econsideration%29%2C%0D%0Aarrow%281%2C0%2C1%2C-10%29%2Carrow%281%2C0%2C1%2C10%29%2C%0D%0Alocate%281.5%2C1%2Cwidth%3C21.9inches%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, let me add the desired location for that microwave, and the microwave entering the constricted space.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-42%2C14%2C-14%2C14%2C%0D%0Aline%28-36%2C-11.75%2C-36%2C11.75%29%2C%0D%0Aline%28-36%2C-11.75%2C0%2C-11.75%29%2C%0D%0Aline%28-36%2C11.75%2C0%2C11.75%29%2C%0D%0Alocate%28-39.5%2C2.5%2C23.5%29%2Clocate%28-41%2C0.5%2Cinches%29%2C%0D%0Aline%280%2C-11.75%2C0%2C-10%29%2C%0D%0Aline%280%2C11.75%2C0%2C10%29%2C%0D%0Aline%280%2C-10%2C2%2C-10%29%2C%0D%0Aline%280%2C10%2C2%2C10%29%2C%0D%0Agreen%28rectangle%28-35.35%2C-10.95%2C-18%2C10.95%29%29%2C%0D%0Ared%28rectangle%28-8.9%2C-8.675%2C13%2C8.675%29%29%2C%0D%0Alocate%28-2%2C8.5%2Cred%2821.9inches%29%29%2C%0D%0Alocate%28-8.5%2C1%2Cred%2817.35inches%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Once that red rectangle enters the space that is 23.5 inches wide,<BR>\n" );
document.write( "you would like to turn it around.<BR>\n" );
document.write( "However, at all times the four corners of that rectangle will be on a circle with a diameter as long as the diagonal of that rectangle.<BR>\n" );
document.write( "According to the Pythagorean theorem, the length of that diagonal, in inches, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2821.9%5E2%2B17.35%5E2%29=sqrt%28479.61%2B301.0225%29=sqrt%28780.6325%29=about27.94 ALIGN=MIDDLE  ALT=\"sqrt%2821.9%5E2%2B17.35%5E2%29=sqrt%28479.61%2B301.0225%29=sqrt%28780.6325%29=about27.94\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "so you need a 28 inch wide space to turn that around.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE 1:<BR>\n" );
document.write( "If that microwave had a really incredibly short height, say 8.5 inches,<BR>\n" );
document.write( "you could enter it on its back (back down, front up).<BR>\n" );
document.write( "Then your red rectangle would be 8.5 inches by 21.9 inches,<BR>\n" );
document.write( "with a diagonal measuring almost 23.5 inches.<BR>\n" );
document.write( "After its length is along the width of the closet, then you could \"log-roll\" it to have the back against the back of the space.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE 2:<BR>\n" );
document.write( "If the floor plan is not exactly like my drawing,<BR>\n" );
document.write( "your easiest solution would be to separately draw to scale on graph paper ( or grid paper)<BR>\n" );
document.write( "1) your floor plan, and<BR>\n" );
document.write( "2) the microwave (top view and front view).<BR>\n" );
document.write( "Cutting out the microwave shapes, you can play with them on the floor plan drawing to see if you can fit it through.<BR>\n" );
document.write( " </SPAN>\n" );
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