document.write( "Question 1022222: An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?\r
\n" ); document.write( "\n" ); document.write( "A) 18.8 cm
\n" ); document.write( "B) 24.2 cm
\n" ); document.write( "C) 42.0 cm
\n" ); document.write( "D) 72.7 cm \n" ); document.write( "

Algebra.Com's Answer #637982 by MathTherapy(10552) $\"\"$ $\"About$

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An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?\r
\n" ); document.write( "\n" ); document.write( "A) 18.8 cm
\n" ); document.write( "B) 24.2 cm
\n" ); document.write( "C) 42.0 cm
\n" ); document.write( "D) 72.7 cm
\n" ); document.write( "

Since 21 is one of the shorter sides, it follows that 2x MUST be the longest side
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document.write( "We then get: 2x < x + 21 
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document.write( "2x - x < 21
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document.write( "x < 21
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document.write( "Therefore, the longest side, or 2x < 42 
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document.write( "Since the longest side, or 2x < 42, then the longest side's length can either be 18.8 cm (choice A), or 24.2 cm (choice B),
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document.write( "but since one of the shorter sides is 21, the  \n" );
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