document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146985>Question 1146985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right triangle has area 84 ft2 and a hypotenuse that is 1 foot longer than one of its sides.<BR>\n" );
document.write( "(a) If x denotes the length of this side, does 2x^3 + x^2 − 28,224 = 0 ?<BR>\n" );
document.write( "(b) Is there a positive root of the equation in part (a) that is less than 28?<BR>\n" );
document.write( "(c) Find the lengths of the sides 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 #768273 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since the area is a whole number and the hypotenuse is 1 foot longer than one of the sides, the side lengths are almost certainly a Pythagorean triple.<br><BR>\n" );
document.write( "One of the smallest Pythagorean triples satisfies all the conditions of the problem; 7-24-25.<br><BR>\n" );
document.write( "The area is (1/2)(7)(24) = 84<BR>\n" );
document.write( "The hypotenuse is 1 foot longer than one of the sides.<br><BR>\n" );
document.write( "Brute force calculations or a calculator show that x=24 is a root of the equation shown in (a).<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "(a) yes; 24 is a root of that equation<BR>\n" );
document.write( "(b) yes; 24 is less than 28<BR>\n" );
document.write( "(c) 7, 24, and 25<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );