document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203399>Question 1203399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, it would be equilateral. Find the length of the base of the original triangle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838934 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=838934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Formal algebra is of course fine for solving the problem; and maybe a formal algebraic solution was wanted.<br><BR>\n" );
document.write( "But the problem looks to me like one for which an informal solution, using logical reasoning and simple arithmetic, is a useful exercise.<br><BR>\n" );
document.write( "When each leg was shortened by 7cm and the base was lengthened by 4cm, the change in the perimeter was 2(-7)+4 = -14+4 = -10.  So the perimeter of the new triangle is 46-10 = 36cm.<br><BR>\n" );
document.write( "The new triangle is equilateral, so each side length is 36/3 = 12cm.<br><BR>\n" );
document.write( "The base of the original triangle was lengthened by 4cm, so the base of the original triangle was 12-4 = 8cm.<br><BR>\n" );
document.write( "ANSWER: 8cm<br><BR>\n" );
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