document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=791763>Question 791763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Perimeter of right angled triangle is 30 cm and hypotenuse is 13 cm. Find the length of other two sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479718 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=479718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This happens to be one of the basic right triangles that I remember, 5:12:13, but to calculate it perform the following steps.<BR>\n" );
document.write( "Let a = one of the legs of the right triangle<BR>\n" );
document.write( "Let b = the other leg<BR>\n" );
document.write( "Then we have<BR>\n" );
document.write( "(1) a + b = 30 - 13 or<BR>\n" );
document.write( "(2) a + b = 17 or<BR>\n" );
document.write( "(3) a = 17 - b<BR>\n" );
document.write( "Now using pythagoreon theorem we have<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+169 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "Now substitute a of (3) into (5) to get<BR>\n" );
document.write( "(6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817-b%29%5E2+%2B+b%5E2+=+169 ALIGN=MIDDLE  ALT=\"%2817-b%29%5E2+%2B+b%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(7) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=289-34%2Ab%2Bb%5E2+%2B+b%5E2+=+169 ALIGN=MIDDLE  ALT=\"289-34%2Ab%2Bb%5E2+%2B+b%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(8) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=289-169-34%2Ab%2B2%2Ab%5E2+=+0 ALIGN=MIDDLE  ALT=\"289-169-34%2Ab%2B2%2Ab%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or using x = b<BR>\n" );
document.write( "(9) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-34%2Ax%2B120+=+0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-34%2Ax%2B120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Use the quadratic equation to solve for x<BR>\n" );
document.write( "(10) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2834+%2B-+sqrt%28+34%5E2-4%2A2%2A120+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%2834+%2B-+sqrt%28+34%5E2-4%2A2%2A120+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "(11)  b = 5,12<BR>\n" );
document.write( "Let's check this with (1) and (4).<BR>\n" );
document.write( "Is (5+12+13 = 30)?<BR>\n" );
document.write( "Is (30 = 30)? Yes<BR>\n" );
document.write( "Is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2+=+5%5E2+%2B+12%5E2 ALIGN=MIDDLE  ALT=\"13%5E2+=+5%5E2+%2B+12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)?<BR>\n" );
document.write( "Is (169 = 25 + 144)?<BR>\n" );
document.write( "Is (169 = 169)? Yes<BR>\n" );
document.write( "Answer: the other two sides (legs) are 5cm and 12cm. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );