document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151211>Question 1151211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 45 in squared . Find the lengths of the sides of the two squares. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772873 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Square A has side length x+3<BR>\n" );
document.write( "Square B has side length x<BR>\n" );
document.write( "Square A has a side length 3 units larger compared to the side length of square B.<BR>\n" );
document.write( "Negative side lengths are not possible, so x > 0.\r<BR>\n" );
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document.write( "Compute the area of square A<BR>\n" );
document.write( "area of square A = (side length of square A)^2<BR>\n" );
document.write( "area of square A = (x+3)^2<BR>\n" );
document.write( "area of square A = (x+3)(x+3)<BR>\n" );
document.write( "area of square A = x(x+3)+3(x+3)<BR>\n" );
document.write( "area of square A = x^2+3x+3x+9<BR>\n" );
document.write( "area of square A = x^2+6x+9<BR>\n" );
document.write( "You could use the FOIL rule to expand out (x+3)^2, but I think the distributive property is more versatile. \r<BR>\n" );
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document.write( "Compute the area of square B<BR>\n" );
document.write( "area of square B = (side length of square B)^2<BR>\n" );
document.write( "area of square B = x^2\r<BR>\n" );
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document.write( "Add up the two areas<BR>\n" );
document.write( "total area = (area of square A)+(area of square B)<BR>\n" );
document.write( "total area = (x^2+6x+9)+(x^2)<BR>\n" );
document.write( "total area = 2x^2+6x+9\r<BR>\n" );
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document.write( "Set this total area equal to 45 and solve for x<BR>\n" );
document.write( "2x^2+6x+9 = 45<BR>\n" );
document.write( "2x^2+6x+9-45 = 0<BR>\n" );
document.write( "2x^2+6x-36 = 0<BR>\n" );
document.write( "2(x^2+3x-18) = 0<BR>\n" );
document.write( "x^2+3x-18 = 0/2<BR>\n" );
document.write( "x^2+3x-18 = 0<BR>\n" );
document.write( "(x+6)(x-3) = 0<BR>\n" );
document.write( "x+6 = 0 or x-3 = 0<BR>\n" );
document.write( "x = -6 or x = 3\r<BR>\n" );
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document.write( "Since x > 0, this means we only consider x = 3 as the solution.<BR>\n" );
document.write( "If x = 3, then x+3 = 3+3 = 6.\r<BR>\n" );
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document.write( "Square A has a side length of 6 inches and an area of 36 square inches.<BR>\n" );
document.write( "Square B has a side length of 3 inches and an area of 9 square inches.<BR>\n" );
document.write( "The total area is 36+9 = 45 square inches.<BR>\n" );
document.write( "The answer checks out.<BR>\n" );
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