document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72991>Question 72991</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve: A rectangle is 6cm long and 5cm wide.  When each dimension is increased by x cm, the area is tripled. Find the value of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52219 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Area A of a rectangle is found by multiplying the length L times the width W.  In this<BR>\n" );
document.write( "problem you are told that the length L is 6 cm and the width W is 5 cm.  Therefore, <BR>\n" );
document.write( "the Area is L times W and this is 6 times 5 = 30 square cm.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next we are going to increase L by x cm, making the new length (6 + x) cm.  We are also going<BR>\n" );
document.write( "to increase W by the same x cm, making the new width (5 + x) cm.  As a result the new <BR>\n" );
document.write( "Area will be 3 times the old area or 3 times 30 square cm which is 90 sq cm.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can write the equation for the new area resulting from the new length times the new width.<BR>\n" );
document.write( "This equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+L+%2A+W ALIGN=MIDDLE  ALT=\"A+=+L+%2A+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90+=+%286%2Bx%29%2A%285%2Bx%29 ALIGN=MIDDLE  ALT=\"90+=+%286%2Bx%29%2A%285%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the right side using the FOIL method (multiply Firsts, Outsides, Insides, then<BR>\n" );
document.write( "Lasts and add them all together).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Firsts = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2A+5+=+30 ALIGN=MIDDLE  ALT=\"6+%2A+5+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Outsides = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax+=+6x ALIGN=MIDDLE  ALT=\"6%2Ax+=+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Insides = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2A+5+=+5x ALIGN=MIDDLE  ALT=\"x+%2A+5+=+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Lasts = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax=+x%5E2 ALIGN=MIDDLE  ALT=\"x%2Ax=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding them all together gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+%2B+6x+%2B+5x+%2B+x%5E2+=+x%5E2+%2B+11x+%2B+30 ALIGN=MIDDLE  ALT=\"30+%2B+6x+%2B+5x+%2B+x%5E2+=+x%5E2+%2B+11x+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This equals the<BR>\n" );
document.write( "new area.  Therefore, set it equal to 90.  When you do the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+11x+%2B+30+=+90 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+%2B+30+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 90 from both sides to eliminate the 90 on the right side.  When you do this subtraction<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+11x+-+60+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+-+60+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that the left side can be factored.  When you do the factoring you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+15%29%2A%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+15%29%2A%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This equation will be true if either of the two factors equals zero because zero times anything<BR>\n" );
document.write( "on the left side will make the left side equal the zero on the right side. So set the<BR>\n" );
document.write( "two factors equal to zero, one at a time.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B15+=+0 ALIGN=MIDDLE  ALT=\"x%2B15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 15 from both sides to eliminate the 15 on the left side.  When you do that you<BR>\n" );
document.write( "get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-15 ALIGN=MIDDLE  ALT=\"x+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This doesn't make sense. Instead of adding to the original dimensions<BR>\n" );
document.write( "we would be taking away from them ... adding a negative 15. So we ignore this solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+4+=+0 ALIGN=MIDDLE  ALT=\"+x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add 4 to both sides to eliminate the -4 on the left side.  This results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B4 ALIGN=MIDDLE  ALT=\"x+=+%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's more like what we might expect. Let's try it by adding 4 cm to each of the original<BR>\n" );
document.write( "dimensions and see what the new area will be.  The original length was 6 cm.  If we add 4 cm<BR>\n" );
document.write( "to it we get a new length of 10 cm.  And the original width was 5 cm.  If we add 4 cm to it<BR>\n" );
document.write( "we get a new width of 9 cm.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The new area will be the new length times the new width or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2A+9+=+90 ALIGN=MIDDLE  ALT=\"10+%2A+9+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Everything checks out so your answer is x = +4 cm.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I hope this helps you to understand the problem better. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );