document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128669>Question 1128669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find, correct to 1 decimal place, the percentage areas for these situations.<BR>\n" );
document.write( "a) The largest square inside a circle.<BR>\n" );
document.write( "b) The largest circle inside a square.<BR>\n" );
document.write( "c) The largest square inside a right isosceles triangle.<BR>\n" );
document.write( "d) The largest circle inside a right isosceles triangle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745305 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5345)</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=745305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A good strategy to calculate the percentages required is to<BR>\n" );
document.write( "assign a length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to a side or a radius,<BR>\n" );
document.write( "because \"scaling up or down\" the drawing for any of the cases<BR>\n" );
document.write( "would not change the ratio of areas of the geometrical figures.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) The largest square inside a circle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.1%2C1.1%2C-1.1%2C1.1%2C%0D%0Acircle%280%2C0%2C1%29%2C%0D%0Agreen%28triangle%28-0.707%2C0.707%2C-0.707%2C-0.707%2C0.707%2C0.707%29%29%2C%0D%0Agreen%28triangle%280.707%2C0.707%2C0.707%2C-0.707%2C-0.707%2C0.707%29%29%2C%0D%0Arectangle%28-0.707%2C-0.707%2C0.707%2C0.707%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the radius of that circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the area of the circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2=pi%2A1%5E2=pi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2=pi%2A1%5E2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "each of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > isosceles right triangles forming the square<BR>\n" );
document.write( "has legs measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and area =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A1%2F2=1%2F2 ALIGN=MIDDLE  ALT=\"1%2A1%2F2=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the area of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The area of the square as a percentage of the area of the square as a fraction/percentage of the area of the circle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fpi ALIGN=MIDDLE  ALT=\"2%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aproximately ALIGN=MIDDLE  ALT=\"aproximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.637=highlight%28%2263.7%25%22%29 ALIGN=MIDDLE  ALT=\"0.637=highlight%28%2263.7%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b) The largest circle inside a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.1%2C1.1%2C-1.1%2C1.1%2C%0D%0Acircle%280%2C0%2C1%29%2C%0D%0Arectangle%28-1%2C-1%2C1%2C1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the radius of that circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the area of the circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2=pi%2A1%5E2=pi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2=pi%2A1%5E2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "the length of the side of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the area of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2=4 ALIGN=MIDDLE  ALT=\"2%2A2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The area of the circle as a fraction/percentage of the area of the square is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aproximately ALIGN=MIDDLE  ALT=\"aproximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.785=highlight%28%2278.5%25%22%29 ALIGN=MIDDLE  ALT=\"0.785=highlight%28%2278.5%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "c) The largest square inside a right isosceles triangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.1%2C2.1%2C-0.1%2C2.1%2C%0D%0Agreen%28triangle%280%2C0%2C1%2C0%2C0%2C1%29%29%2C%0D%0Atriangle%280%2C0%2C2%2C0%2C0%2C2%29%2C%0D%0Arectangle%280%2C0%2C1%2C1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 4 small congruent triangles inside the large right isosceles triangle,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of those small triangles forming the square,<BR>\n" );
document.write( "so the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4=1%2F2=highlight%28%2250.0%25%22%29 ALIGN=MIDDLE  ALT=\"2%2F4=1%2F2=highlight%28%2250.0%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the triangle.<BR>\n" );
document.write( " <BR>\n" );
document.write( "d) The largest circle inside a right isosceles triangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.1%2C2.5%2C-1.1%2C2.58%2C%0D%0Acircle%280%2C0%2C1%29%2C%0D%0Agreen%28triangle%280%2C0%2C0%2C-1%2C-1%2C-1%29%29%2C%0D%0Agreen%28triangle%280%2C0%2C-1%2C0%2C-1%2C2.414%29%29%2C%0D%0Agreen%28triangle%280%2C0%2C2.414%2C-1%2C0.707%2C0.707%29%29%2C%0D%0Ared%28triangle%28-1%2C-1%2C2.414%2C-1%2C0%2C0%29%29%2C%0D%0Ared%28triangle%28-1%2C-1%2C-1%2C2.414%2C0%2C0%29%29%2C%0D%0Atriangle%28-1%2C-1%2C-1%2C2.414%2C2.414%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the radius of that circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the length of each leg of the right isosceles triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the area of the circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2=pi%2A1%5E2=pi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2=pi%2A1%5E2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the area of the triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2As%2F2=s%5E2%2F2 ALIGN=MIDDLE  ALT=\"s%2As%2F2=s%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The right isosceles triangle is made of three smaller triangles,<BR>\n" );
document.write( "each with height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and each having for a base one side of the right isosceles triangle.<BR>\n" );
document.write( "Two of those triangles have a base of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the area of each one of those is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2Ar%2F2=s%2F2 ALIGN=MIDDLE  ALT=\"s%2Ar%2F2=s%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The third small triangle has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29s ALIGN=MIDDLE  ALT=\"sqrt%282%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a base,<BR>\n" );
document.write( "and its area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29s%2Ar%2F2=sqrt%282%29s%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29s%2Ar%2F2=sqrt%282%29s%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The areas of those three small triangles adds up to the area of the right isosceles triangle, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2F2=s%2F2%2Bs%2F2%2Bsqrt%282%29s%2F2 ALIGN=MIDDLE  ALT=\"s%5E2%2F2=s%2F2%2Bs%2F2%2Bsqrt%282%29s%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "multiplying both sides of the equal sign times 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=s%2Bs%2Bsqrt%282%29s ALIGN=MIDDLE  ALT=\"s%5E2=s%2Bs%2Bsqrt%282%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=2s%2Bsqrt%282%29s ALIGN=MIDDLE  ALT=\"s%5E2=2s%2Bsqrt%282%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=2%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"s=2%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the area of the right isosceles triangle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2F2=%282%2Bsqrt%282%29%29%5E2%2F2=%284%2B2%2B4sqrt%282%29%29%2F2=%286%2B4sqrt%282%29%29%2F2=3%2B2sqrt%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The area of the circle as a fraction/percentage of the area of the right isosceles triangle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F%283%2B2sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"pi%2F%283%2B2sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aproximately ALIGN=MIDDLE  ALT=\"aproximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.539=highlight%28%2253.9%25%22%29 ALIGN=MIDDLE  ALT=\"0.539=highlight%28%2253.9%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );