document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191970>Question 1191970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an isosceles triangle ABC, side AB is twice as long as AC. The perimeter of the triangle is 200cm. Find the length of AC. <BR>\n" );
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document.write( "x = length of side AC<BR>\n" );
document.write( "2x = length of side AB, since it's twice as long as AC\r<BR>\n" );
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document.write( "Triangle ABC is isosceles, meaning there are exactly two sides that are the same length.<BR>\n" );
document.write( "We've already ruled out AB and AC being the same length.\r<BR>\n" );
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document.write( "It's not clear if BC = AC or if BC = AB\r<BR>\n" );
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document.write( "Both cases cannot be true simultaneously. Why not? Because that would lead to the false statement that AB = AC, when it should be AB > AC.\r<BR>\n" );
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document.write( "If BC = AC, then BC = x and,<BR>\n" );
document.write( "AB+BC+AC = perimeter<BR>\n" );
document.write( "2x+x+x = 200<BR>\n" );
document.write( "4x = 200<BR>\n" );
document.write( "x = 200/4<BR>\n" );
document.write( "x = 50<BR>\n" );
document.write( "So AC = 50\r<BR>\n" );
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document.write( "Or if BC = AB, then BC = 2x and,<BR>\n" );
document.write( "AB+BC+AC = perimeter<BR>\n" );
document.write( "2x+2x+x = 200<BR>\n" );
document.write( "5x = 200<BR>\n" );
document.write( "x = 200/5<BR>\n" );
document.write( "x = 40<BR>\n" );
document.write( "meaning that AC = 40\r<BR>\n" );
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document.write( "So there are two possibilities:<BR>\n" );
document.write( "Either AC = 50 or AC = 40<BR>\n" );
document.write( "depending on which two sides are equal of this isosceles triangle.\r<BR>\n" );
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document.write( "Currently there isn't enough information to determine which of those values is the correct AC length.<BR>\n" );
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