document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642613>Question 642613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height of a right-angled triangle is 1 m more than its base and its hypotenuse is 2 m more than its base. Find the height 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 #404199 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=404199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the length of the base, in meters.<BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1 ALIGN=MIDDLE  ALT=\"b%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height, in meters, and<BR>\n" );
document.write( "the length of the hypotenuse, in meters is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B2 ALIGN=MIDDLE  ALT=\"b%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Any of the sides of a triangle can be called the base,<BR>\n" );
document.write( "but in this case, we know that it is not the hypotenuse,<BR>\n" );
document.write( "because the problem says that the hypotenuse is 2 m longer than the base.<BR>\n" );
document.write( "So the base is one of the leg of the right triangle.<BR>\n" );
document.write( "The other leg, being perpendicular is the height.<BR>\n" );
document.write( "Using the Pythagorean relationship between the lengths of the legs and the hypotenuse of a right triangle, we can write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B%28b%2B1%29%5E2=%28b%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2B%28b%2B1%29%5E2=%28b%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we simplify the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B%28b%2B1%29%5E2=%28b%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2B%28b%2B1%29%5E2=%28b%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bb%5E2%2B2b%2B1=b%5E2%2B4b%2B4 ALIGN=MIDDLE  ALT=\"b%5E2%2Bb%5E2%2B2b%2B1=b%5E2%2B4b%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bb%5E2%2B2b%2B1-b%5E2-4b-4=b%5E2%2B4b%2B4-b%5E2-4b-4 ALIGN=MIDDLE  ALT=\"b%5E2%2Bb%5E2%2B2b%2B1-b%5E2-4b-4=b%5E2%2B4b%2B4-b%5E2-4b-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-2b-3=0 ALIGN=MIDDLE  ALT=\"b%5E2-2b-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we solve the quadratic equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The easiest way is factoring the quadratic polynomial on the left hand side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-2b-3=0 ALIGN=MIDDLE  ALT=\"b%5E2-2b-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B1%29%28b-3%29=0 ALIGN=MIDDLE  ALT=\"%28b%2B1%29%28b-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions to the equation are the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > that make one of those factors zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1=0 ALIGN=MIDDLE  ALT=\"b%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1 ALIGN=MIDDLE  ALT=\"b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution of the equation, but a negative number cannot be the length of the base of a triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-3=0 ALIGN=MIDDLE  ALT=\"b-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only solution for the length of the base of the triangle.<BR>\n" );
document.write( "Then, the height, in meters is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1=3%2B1=highlight%284%29 ALIGN=MIDDLE  ALT=\"b%2B1=3%2B1=highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The triangle has side length in the ratio 3:4:5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2%2B4%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"3%5E2%2B4%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and (3,4,5) is the most popular of the Pythagorean triples.<BR>\n" );
document.write( "Teachers love it and it is the only one I remember. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );