document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855606>Question 855606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question: An artist used silver wire to make a triangle that has a perimeter of 30 inches. Shen then used copper wire to make the largest circle that could fit in the triangle.<BR>\n" );
document.write( "how many more inches of silver wire did the artist use compared to copper wire? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515507 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=515507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The center of the circle inscribed in the triangle is the incenter, the point at the same distance from all 3 sides.<BR>\n" );
document.write( "It can be found as the intersection of the angle bisectors (all 3 intersect there, but we can find the incenter by drawing any two of them).<BR>\n" );
document.write( " <BR>\n" );
document.write( "If I were the artist my triangle would be an equilateral triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-6%2C6%2C-2%2C10%2C%0D%0Agreen%28rectangle%280%2C0%2C0.4%2C0.4%29%29%2Ctriangle%28-5%2C0%2C5%2C0%2C0%2C8.66%29%2C%0D%0Agreen%28circle%280%2C2.89%2C0.1%29%29%2Cgreen%28line%280%2C2.89%2C5%2C0%29%29%2C%0D%0Agreen%28line%280%2C2.89%2C-5%2C0%29%29%2Cgreen%28line%280%2C2.89%2C0%2C8.66%29%29%2C%0D%0Ared%28circle%280%2C2.89%2C2.89%29%29%2C%0D%0Agreen%28arrow%280%2C0%2C0%2C15%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "An equilateral triangle with a perimeter of 30 inches would have a side length of 10 inches.<BR>\n" );
document.write( "In an equilateral triangle, the height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the length of the side.<BR>\n" );
document.write( "In an equilateral triangle, connecting the incenter to the vertices splits the triangle into 3 congruent triangles.<BR>\n" );
document.write( "They all have the same base as the equilateral triangle,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of the equilateral triangle.<BR>\n" );
document.write( "As a consequence their heights are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the height of the equilateral triangle.<BR>\n" );
document.write( "Those heights, measured perpendicular to the sides to the incenter are the radius of the inscribed circle.<BR>\n" );
document.write( "In my triangle the side measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >inches;<BR>\n" );
document.write( "the height of the equilateral triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%283%29%2F2=5sqrt%283%29 ALIGN=MIDDLE  ALT=\"10sqrt%283%29%2F2=5sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches,<BR>\n" );
document.write( "and the radius of the inscribed circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A%285sqrt%283%29%29=5sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A%285sqrt%283%29%29=5sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The circumference of the circle would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A5sqrt%283%29%2F3=10pi%2Asqrt%283%29%2F3=18.14 ALIGN=MIDDLE  ALT=\"2%2Api%2A5sqrt%283%29%2F3=10pi%2Asqrt%283%29%2F3=18.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches (rounding).<BR>\n" );
document.write( "If the artist uses 30 inches of silver wire for the triangle,<BR>\n" );
document.write( "and 18.14 inches of copper wire for the circle,<BR>\n" );
document.write( "she used <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-18.14=highlight%2811.86%29 ALIGN=MIDDLE  ALT=\"30-18.14=highlight%2811.86%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > more inches of silver wire than of copper wire. </SPAN>\n" );
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