document.write( "Question 1110384: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has a side that is 20 cm and a second that is 4 cm less than twice the third side, what are the possible lengths for the second and third side? \n" ); document.write( "

Algebra.Com's Answer #725561 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The side lengths are 20, x, and 2x-4.

\n" ); document.write( "(1) If 20 is the long side, then
\n" ); document.write( " $\"x%2B2x-4+%3E+20\"$
\n" ); document.write( " $\"3x-4+%3E+20\"$
\n" ); document.write( " $\"3x+%3E+24\"$
\n" ); document.write( " $\"x+%3E+8\"$

\n" ); document.write( "x has to be greater than 8.

\n" ); document.write( "To verify that this is a limiting value, note that if x=8 the sides are 20, 8, and 12, and the sum of the two short side lengths is exactly equal to the long side.

\n" ); document.write( "(2) If 2x-4 is the long side, then
\n" ); document.write( " $\"20%2Bx+%3E+2x-4\"$
\n" ); document.write( " $\"24+%3E+x\"$ >br>
\n" ); document.write( "x has to be less than 24.

\n" ); document.write( "Again letting x be 24 we get side lengths of 20, 24, and 44; and again the sum of the two short side lengths is exactly equal to the long side.

\n" ); document.write( "Answer: x can be any number greater than 8 and less than 24. \n" ); document.write( "

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