document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77435>Question 77435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1) The perimeter of a rectangle is 100 and its diagonal has length \"x\". The area of this rectangle,is<BR>\n" );
document.write( "(A) 625-x^2   (b) 625-(x^2)/2   (c) 1250-x^2 (d) 1250-(x^2)/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55542 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=55542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perimeter(P)=two times length (L) plus two times width (W) or\r<BR>\n" );
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document.write( "P=2L+2W<BR>\n" );
document.write( "2L+2W=100 divide both sides by 2 <BR>\n" );
document.write( "L+W=50-----------------------------------eq1\r<BR>\n" );
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document.write( "Area of rectangle (A)=length(L)*width(W) or\r<BR>\n" );
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document.write( "A=L*W-------------------------------------eq2\r<BR>\n" );
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document.write( "When we draw the diagonal in a rectangle we, in effect, divide the rectangle into two identical right triangles. Here, we can apply the Pythagorean Theorem:\r<BR>\n" );
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document.write( "L^2+W^2=x^2--------------------------------eq3\r<BR>\n" );
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document.write( "Clearly, we have enough information to solve these non-linear simultaneous equations----BUT THAT'S NOT RECOMMENDED!  Instead, lets square both sides of eq1 and we get:\r<BR>\n" );
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document.write( "(L+W)^2=50^2<BR>\n" );
document.write( "L^2+2L*W+W^2=2500  lets rewrite this:\r<BR>\n" );
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document.write( "L^2+W^2+2L*W=2500 but<BR>\n" );
document.write( "L^2+W^2=x^2 and<BR>\n" );
document.write( "L*W=A\r<BR>\n" );
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document.write( "substitute these into the equation and we get:\r<BR>\n" );
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document.write( "x^2+2A=2500  subtract x^2 from both sides\r<BR>\n" );
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document.write( "x^2-x^2+2A=2500-x^2  collect like terms\r<BR>\n" );
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document.write( "2A=2500-x^2  divide both sides by 2\r<BR>\n" );
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document.write( "A=(2500-x^2)/2<BR>\n" );
document.write( "A=1250-(x^2)/2--------------------------------ans\r<BR>\n" );
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document.write( "Frequently, when a problem appears much too difficult, there will be an easy way to solve it\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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