document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=732967>Question 732967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Well my question is the length of a triangle is increased by 1 unti its width is decreased by 1 unit what happens to the area and perimeter. \r<BR>\n" );
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document.write( "what i have so far is i think that if you add one then subtract one the length and the width would stay the same like equivalent  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448279 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=448279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rectangles have 4 right angles, a length and width. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1%2C29%2C-2%2C18%2C%0D%0Arectangle%280%2C0%2C28%2C16%29%2Clocate%2811%2C0%2Clength%29%2C%0D%0Alocate%2818%2C9%2Cwidth%29%2Carrow%2820%2C7.5%2C20%2C0%29%2Carrow%2820%2C9%2C20%2C16%29%2C%0D%0Aarrow%2810.5%2C-1%2C0%2C-1%29%2Carrow%2816.5%2C-1%2C28%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The length is the measure of the longest side. In the units I chose, the length of that rectangle is 7 and the width is 4.<BR>\n" );
document.write( "The perimeter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B4%2B7%2B4=22 ALIGN=MIDDLE  ALT=\"7%2B4%2B7%2B4=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > of my units and<BR>\n" );
document.write( "the area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A4=28 ALIGN=MIDDLE  ALT=\"7%2A4=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units<BR>\n" );
document.write( "In a rectangle, if you increase the length by 1 unit and decrease the width by 1 unit, the perimeter stays the same, and the area gets smaller.The change in area depends on the original dimensions.<BR>\n" );
document.write( "If I increase length of my rectangle to 8 and decrease its width to 3,<BR>\n" );
document.write( "perimeter=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B3%2B8%2B3=22 ALIGN=MIDDLE  ALT=\"8%2B3%2B8%2B3=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and area=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A3=24 ALIGN=MIDDLE  ALT=\"8%2A3=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Triangles do not have a \"length\" and \"width\".<BR>\n" );
document.write( "You can choose one of the 3 sides as the base; set the triangle on that side; measure the length of the side called base, and measure the height perpendicular to that base. Someone may rotate the triangle and have a different base and height for the same triangle, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.7%2C6.3%2C-0.7%2C6.3%2C%0D%0Atriangle%280%2C0%2C5%2C0%2C3.2%2C2.4%29%2Ctriangle%280%2C2.5%2C4%2C2.5%2C0%2C5.5%29%2C%0D%0Ared%28line%280%2C2.5%2C0%2C5.5%29%29%2Cred%28rectangle%280%2C2.5%2C0.2%2C2.7%29%29%2C%0D%0Ared%28line%283.2%2C0%2C3.2%2C2.4%29%29%2Cred%28rectangle%283.2%2C0%2C3.4%2C0.2%29%29%2C%0D%0Alocate%281.5%2C2.9%2Cbase%29%2Clocate%280.1%2C4.3%2Cred%28height%29%29%2C%0D%0Alocate%282.15%2C0%2Cbase%29%2Clocate%283.3%2C0.9%2Cred%28height%29%29%2C%0D%0Aarrow%282%2C-0.2%2C0%2C-0.2%29%2Carrow%283%2C-0.2%2C5%2C-0.2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > There are 2 copies of the same triangle in that figure. A different side is chosen as base in each one, and the height is measured perpendicular to the chosen base.<BR>\n" );
document.write( "If you increase the base by 1 unit and decrease the height by 1 unit, the perimeter and the area change in ways that depend on the original dimensions.<BR>\n" );
document.write( "The triangles in my drawing have side lengths of 3, 4, and 5 of my units for that drawing.<BR>\n" );
document.write( "For the top triangle I chose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=base=4 ALIGN=MIDDLE  ALT=\"base=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height=3 ALIGN=MIDDLE  ALT=\"height=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For the bottom triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=base=5 ALIGN=MIDDLE  ALT=\"base=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height=2.1 ALIGN=MIDDLE  ALT=\"height=2.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The perimeter of the triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B4%2B5=12 ALIGN=MIDDLE  ALT=\"3%2B4%2B5=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=base%2Aheight%2F2 ALIGN=MIDDLE  ALT=\"base%2Aheight%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and can be calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3%2F2=6 ALIGN=MIDDLE  ALT=\"4%2A3%2F2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the top triangle,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A2.4%2F2=12 ALIGN=MIDDLE  ALT=\"5%2A2.4%2F2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the rotated version at the bottom.<BR>\n" );
document.write( "If I increase each base by 1 unit and decrease the corresponding height by 1 unit, I get this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.7%2C6.3%2C-0.7%2C6.3%2C%0D%0Atriangle%280%2C0%2C6%2C0%2C3.84%2C1.4%29%2Ctriangle%280%2C2.5%2C5%2C2.5%2C0%2C4.5%29%2C%0D%0Ared%28line%280%2C2.5%2C0%2C4.5%29%29%2Cred%28rectangle%280%2C2.5%2C0.2%2C2.7%29%29%2C%0D%0Ared%28line%283.84%2C0%2C3.84%2C1.4%29%29%2Cred%28rectangle%283.84%2C0%2C4.04%2C0.2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The triangles are no longer the same triangle.<BR>\n" );
document.write( "For the top triangle the side length are now 5, 2, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2829%29=about+5.385 ALIGN=MIDDLE  ALT=\"sqrt%2829%29=about+5.385\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The perimeter is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B2%2B5.385=12.385 ALIGN=MIDDLE  ALT=\"5%2B2%2B5.385=12.385\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A2%2F2=5 ALIGN=MIDDLE  ALT=\"5%2A2%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The bottom triangle now has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=base=6 ALIGN=MIDDLE  ALT=\"base=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height=1.4 ALIGN=MIDDLE  ALT=\"height=1.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sides measure 6, about 4.087, and about 4.406.<BR>\n" );
document.write( "The new perimeter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B4.087%2B4.406=14.493 ALIGN=MIDDLE  ALT=\"6%2B4.087%2B4.406=14.493\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The new area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A1.4%2F2=4.2 ALIGN=MIDDLE  ALT=\"6%2A1.4%2F2=4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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