document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040515>Question 1040515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a rectangle is 10 inches and the area is 45 square inches. Find the dimensions of the triangle, correct to one decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655335 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let l be length and w be width of the rectangle, then<BR>\n" );
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document.write( "1) l^2 + w^2 = 10^2<BR>\n" );
document.write( "2) l * w = 45<BR>\n" );
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document.write( "we have two equations in two unknowns<BR>\n" );
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document.write( "solve 2 for l and substitute in 1<BR>\n" );
document.write( "l = 45/w<BR>\n" );
document.write( "(45/w)^2 + w^2 = 100<BR>\n" );
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document.write( "(2025/w^2) + w^2 = 100<BR>\n" );
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document.write( "multiply both sides of = by w^2<BR>\n" );
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document.write( "2025 + w^4 = 100w^2<BR>\n" );
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document.write( "w^4 -100w^2 + 2045 = 0<BR>\n" );
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document.write( "let u = w^2<BR>\n" );
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document.write( "u^2 -100u + 2025 = 0<BR>\n" );
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document.write( "use quadratic equation<BR>\n" );
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document.write( "u = (100 + square root( (-100)^2 - 4(1)(2025) ) ) / 2 = 71.8<BR>\n" );
document.write( "u = (100 - square root( (-100)^2 - 4(1)(2025) ) ) / 2 = 28.2<BR>\n" );
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document.write( "since u = w^2, we have<BR>\n" );
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document.write( "w^2 = 71.8 and w = 8.5 <BR>\n" );
document.write( "w^2 = 28.2 and w = 5.3<BR>\n" );
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document.write( "we have 2 solutions for l as well<BR>\n" );
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document.write( "l = 45/8.5 = 5.3<BR>\n" );
document.write( "l = 45/5.3 = 8.5<BR>\n" );
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document.write( "Our 2 solutions are<BR>\n" );
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document.write( "w = 8.5 and l = 5.3<BR>\n" );
document.write( "w = 5.3 and l = 8.5<BR>\n" );
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document.write( "note that <BR>\n" );
document.write( "8.5 * 5.3 = 45.05<BR>\n" );
document.write( "8.5^2 + 5.3^2 = 100.34 and square root of 100.34 = 10.02<BR>\n" );
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