document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270960>Question 270960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello tutor my name is faisal and i have 2 important questions to ask u<BR>\n" );
document.write( "1) if the perimeter of a right traingle is 3 meters and the hypotenuse is 145 cm, what is the length of the other 2 sides.<BR>\n" );
document.write( "2) A picture's area is 10cm by 8cm and the width is also uniform, it is going to be placed on a mat that is twice the area of the picture, what is the width of the mat? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198404 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=198404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "#1:  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the measure of one leg of your triangle.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> represent the measure of the other leg.  Since the perimeter is 3 meters, which is to say 300 cm, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 145\ +\ x\ +\ y\ = 300\">\r<BR>\n" );
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document.write( "It will be convenient to solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> at this point:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ = 155\ -\ x\">\r<BR>\n" );
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document.write( "Since this is a right triangle, we can also write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ =\ 145^2\">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \left(155\ -\ x\right)^2\ =\ 145^2\">\r<BR>\n" );
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document.write( "Just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  You will get two positive roots, one will be one leg of the triangle and the other root will be the other leg of the triangle.\r<BR>\n" );
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document.write( "#2:   Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the width of the mat.  If the picture is 10 by 8, the mat has to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10\ +\ 2x\"> by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8\ +\ 2x\">.\r<BR>\n" );
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document.write( "Now the only question is whether the area of the mat mentioned in the problem is the overall area of the mat before you cut the hole for the picture, or the area that remains after you cut the hole for the picture.\r<BR>\n" );
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document.write( "If it is the first way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(10\ +\ 2x\right)\left(8\ +\ 2x\right)\ =\  2\cdot 10\cdot 8\ =\ 160\">\r<BR>\n" );
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document.write( "which simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4x^2\ +\ 36x\ -\ 80\ =\ 0\">\r<BR>\n" );
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document.write( "if it is the second way (and this is probably the correct interpretation):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(10\ +\ 2x\right)\left(8\ +\ 2x\right)\ -\ 80\ =\ 160\">\r<BR>\n" );
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document.write( "Which simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4x^2\ +\ 36x\ -\ 320\ =\ 0\">\r<BR>\n" );
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document.write( "Either way, solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  Either way you get a positive and a negative root.  Discard the negative root because you are looking for a positive measure of length.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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