document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266509>Question 266509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right triangle has sides of integer length and perimeter 2010 units. The length of the shortest side is equal to one-fifth of the sum of the lengths of the other two sides. What is the area of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195804 by </B><A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><B>vksarvepalli(154)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><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=vksarvepalli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the sides be a,b & c with a being the shortest and c the hypotenuse(longest)\r<BR>\n" );
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document.write( "the are of the triangle will be 1/2*a*b  (half*base*height)\r<BR>\n" );
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document.write( "given  \r<BR>\n" );
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document.write( "The length of the shortest side is equal to one-fifth of the sum of the lengths of the other two sides\r<BR>\n" );
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document.write( "so a=1/5 *(b+c)\r<BR>\n" );
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document.write( "=> 5a=b+c      ------------------ 1\r<BR>\n" );
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document.write( "and perimeter = 2010 units\r<BR>\n" );
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document.write( "so a+b+c = 2010\r<BR>\n" );
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document.write( "but from 1 \r<BR>\n" );
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document.write( "we get a+5a=2010\r<BR>\n" );
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document.write( "so 6a=2010\r<BR>\n" );
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document.write( "so a=335\r<BR>\n" );
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document.write( "and b+c=5a=1675\r<BR>\n" );
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document.write( "now in a right triangle fro Pythagoras theorem we have\r<BR>\n" );
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document.write( "c^2 = a^2+b^2\r<BR>\n" );
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document.write( "=> c^2-b^2=a^2<BR>\n" );
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document.write( "=> c^2-b^2=335*335\r<BR>\n" );
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document.write( "=> (c-b)(c+b)=335*335\r<BR>\n" );
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document.write( "but c+b = 1675\r<BR>\n" );
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document.write( "so (c-b)*1675=335*335\r<BR>\n" );
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document.write( "so c-b = 67<BR>\n" );
document.write( "   c+b= 1675\r<BR>\n" );
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document.write( "subtracting the above two we get \r<BR>\n" );
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document.write( "2b=1608  so b= 804\r<BR>\n" );
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document.write( "thus area=1/2 * 335 * 804\r<BR>\n" );
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document.write( "therefore  area of the triangle=134670 sq. units </SPAN>\n" );
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