document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241559>Question 241559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a rectangle and a trapezoid have equal areas, then they must have the same<BR>\n" );
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document.write( "A) True<BR>\n" );
document.write( "B) False </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176909 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would have to say no.\r<BR>\n" );
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document.write( "This is because I found one instance where the areas are equal and the perimeters are not.   That's all that's required to destroy the theory.\r<BR>\n" );
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document.write( "Consider that a parallelogram and a trapezoid both are composed of a square in the middle plus two triangles hanging at each end.\r<BR>\n" );
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document.write( "I created two squares with 4 inches on each side.\r<BR>\n" );
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document.write( "I then attached a triangle to the parallelogram on each end so that the resulting structure formed the parallelogram.\r<BR>\n" );
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document.write( "each triangle was a 3/4/5 triangle.\r<BR>\n" );
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document.write( "The one on the left had the 3 on top and the one on the right had the 3 on the bottom.\r<BR>\n" );
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document.write( "The 5 of each triangle was the sides of the parallelogram.\r<BR>\n" );
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document.write( "the other sides of the parallelogram were formed from the 3 and the 5.\r<BR>\n" );
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document.write( "A picture at the end will show you what I mean.\r<BR>\n" );
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document.write( "The trapezoid was formed from the square with two triangles attached to it, 1 on each end.\r<BR>\n" );
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document.write( "1 triangle was a 4/5/sqrt(41) triangle, and the other triangle was a 1/4/sqrt(17) triangle.\r<BR>\n" );
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document.write( "The construction was such that the areas of the trapezoid and the parallelogram were equal.\r<BR>\n" );
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document.write( "They are equal when b*h of the parallelogram = ((b1+b2)/2)*h of the trapezoid.\r<BR>\n" );
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document.write( "Since I made h of the parallelogram equal to h of the trapezoid, this meant that (b1+b2)/2 of the trapezoid equal to b of the parallelogram.\r<BR>\n" );
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document.write( "I calculated the areas and they are equal.\r<BR>\n" );
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document.write( "b of the parallelogram is equal to 7 (4 + 3)\r<BR>\n" );
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document.write( "b1 + b2 of the trapezoid = 4 + 10 = 14\r<BR>\n" );
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document.write( "7*4 = 14/2*4 confirming the areas are equal.\r<BR>\n" );
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document.write( "The perimeters, however, were not equal.\r<BR>\n" );
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document.write( "7+7+5+5 of the parallelogram did not equal to 4+10+sqrt(41)+sqrt(17) of the trapezoid.\r<BR>\n" );
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document.write( "Theory doesn't hold.\r<BR>\n" );
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document.write( "Perimeters are not equal.\r<BR>\n" );
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document.write( "Picture of the resulting structures can be seen <a  rel=nofollow HREF= \"http://theo.x10hosting.com/problems/241559.html\" target = \"_blank\">HERE !!!!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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