Algebra.Com's Answer #810412 by ikleyn(52802)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "The sides of an equilateral triangle  are shortened by 12 units, 13 units, and 14 units
\n" );
document.write( "respectively and a right Angle triangle is formed. I need to find the length of each side of the equilateral triangle
\n" );
document.write( "~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "The Pythagoras says\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "  +  =  ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and it is what you should solve to find x, the side length of the equilateral triangle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Can you guess, how I determined that (x-14) and (x-13) are the legs ?\r\n" );
document.write( "\r\n" );
document.write( " - Because the hypotenuse is the longest side.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, one way for you is to solve this quadratic equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " But it is a long and BORING WAY.\r\n" );
document.write( "\r\n" );
document.write( " There is another, more quick way.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indeed, there is only one appropriate right angle triangle\r\n" );
document.write( "for which one leg is one unit longer than the shortest leg\r\n" );
document.write( "and the hypotenuse is one unit longer than the longest leg.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is (3,4,5) - right angled triangle,\r\n" );
document.write( "\r\n" );
document.write( " so x-12 = 5 and x = 17.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. The side length of the equilateral triangle is 17 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK. (17-13)^2 + (17-14)^2 = 4^2 + 3^2 = 16 + 9 = 25 = 5^2 = (17-12)^2.\r\n" );
document.write( " \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Solved, and you know two ways to solve it: one formal and another informal (quick).\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "-------------\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Actually, it is a joke problem, so I presented the solution to you in this joking form.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "/////////////\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |