document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198847>Question 198847</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321448040/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Directions state:  Find the perimeters and areas of the squares and rectangles in questions 7-10.\r<BR>\n" );
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document.write( "The figure shown in the text has a picture of a square which is dissected in the middle to form two right triangles. The triangle has two 45 degree and one 90 degree angles.  All that is given is six square root of two (6 square root 2) for the hypotenuse of the adjacent right triangles. My apoogies but I do not have a square root symbol key on my computer keyboard.  As you can tell I need to solve for the perimeter and area, but I do not even know how to without data given for either side one or side two. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149326 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=149326\">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( "Since it is a square, the triangle formed by two adjacent sides of the square and the diagonal is an isosceles right triangle -- observation confirmed by the fact that you say it is a 90°-45°-45° triangle.  All isosceles right triangles are similar, that is to say that their sides are in proportion.\r<BR>\n" );
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document.write( "If you have an isosceles right triangle whose legs measure 1 unit, then the Pythagorean Theorem says the hypotenuse is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c = \sqrt{1^2+1^2} = \sqrt{2}\">\r<BR>\n" );
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document.write( "That means that the three sides of any isosceles right triangle are in proportion:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1:1:\sqrt{2}\">\r<BR>\n" );
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document.write( "So, if your hypotenuse, i.e. the diagonal of the square, measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6\sqrt{2}\">, then the two legs must each measure 6 because\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6:6:6\sqrt{2}\">\r<BR>\n" );
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document.write( "is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1:1:\sqrt{2}\">\r<BR>\n" );
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document.write( "Can you take it from there?\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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