document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110820>Question 110820</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80811 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=80811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the shorter leg is x, then the longer leg is twice that plus 4. So the two legs are:<BR>\n" );
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document.write( "x and<BR>\n" );
document.write( "2x + 4<BR>\n" );
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document.write( "In a right triangle the base can be one leg and this makes the other leg the height.<BR>\n" );
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document.write( "The equation for the area of a triangle is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29%2Ab%2Ah ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29%2Ab%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For this problem A = 120 sq inches, b = x inches, and h = 2x + 4 inches.<BR>\n" );
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document.write( "Substituting these values into the area equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+=+%281%2F2%29%2Ax+%2A%282x+%2B+4%29 ALIGN=MIDDLE  ALT=\"120+=+%281%2F2%29%2Ax+%2A%282x+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+=+%281%2F2%29%2A%282x%5E2+%2B+4x%29+=+x%5E2+%2B+2x ALIGN=MIDDLE  ALT=\"120+=+%281%2F2%29%2A%282x%5E2+%2B+4x%29+=+x%5E2+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Transpose the equation (switch sides) to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+=+120 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 120 on the right side by subtracting 120 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+120+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the left side of the equation factors and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+12%29%2A%28x+-+10%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+12%29%2A%28x+-+10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation will be true if either of the two factors on the left side is zero because<BR>\n" );
document.write( "multiplication by zero results in zero ... making the left side equal to the zero on the<BR>\n" );
document.write( "right side.<BR>\n" );
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document.write( "So, one at a time, set each factor equal to zero. <BR>\n" );
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document.write( "First <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+12+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this by subtracting 12 from each side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-12 ALIGN=MIDDLE  ALT=\"x+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This can't be the answer because having a leg equal to a negative value makes no sense.<BR>\n" );
document.write( "So proceed to set the second factor equal to zero:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+10+=+0 ALIGN=MIDDLE  ALT=\"x+-+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this by adding 10 to each side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+10 ALIGN=MIDDLE  ALT=\"+x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This solution tells you that the short leg is 10 inches long. And this means that the <BR>\n" );
document.write( "longer leg is 2*10 + 4 = 20 + 4 = 24 inches. <BR>\n" );
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document.write( "So the two legs are 10 inches and 24 inches.<BR>\n" );
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document.write( "Check: <BR>\n" );
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document.write( "The area has to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A10%2A24+=+5%2A24+=+120 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A10%2A24+=+5%2A24+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" > sq inches. This checks.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
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document.write( " </SPAN>\n" );
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