document.write( "Question 568114: A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is
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Algebra.Com's Answer #366851 by Edwin McCravy(20055) $\"\"$ $\"About$

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A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is
\n" ); document.write( "N square centimeters , where N is a prime number. What is the greatest possible
\n" ); document.write( "value of N?
\n" ); document.write( "Choose one answer:
\n" ); document.write( "a. 12
\n" ); document.write( "b. 11
\n" ); document.write( "c. 9
\n" ); document.write( "d. 2
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document.write( "You can rule out choices a. 12 and c. 9 immediately because they\r\n" );
document.write( "are not prime numbers.  You can also rule out choice d. 2, because\r\n" );
document.write( "when two sides of a triangle are given, the third side must be greater \r\n" );
document.write( "than the difference of the other two sides, and 2 is equal to 6-4, and it\r\n" );
document.write( "would have to be greater than 2.  So that only leaves b. 11, which is a\r\n" );
document.write( "prime number.  \r\n" );
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document.write( "However, it may not be satisfactory to do it entirely by eliminating\r\n" );
document.write( "the wrong choices.  Here is how you would find the answer if you \r\n" );
document.write( "had not been given any choices at all:\r\n" );
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document.write( "Area = ×base×height\r\n" );
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document.write( "N = ×6×h\r\n" );
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document.write( "N = 3h\r\n" );
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document.write( " = sin(q)\r\n" );
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document.write( "h = 4sin(q)\r\n" );
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document.write( "And since N = 3h\r\n" );
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document.write( "N = 3×4sin(q)\r\n" );
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document.write( "N = 12sin(q)\r\n" );
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document.write( "Divide both sides by 12\r\n" );
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document.write( " = sin(q)\r\n" );
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document.write( "The sine of an angle must be 1 or less.  Therefore the largest\r\n" );
document.write( "prime number N could be and  be less than or equal 1 \r\n" );
document.write( "is when N = the prime number 11.\r\n" );
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document.write( "Answer: b. 11 \r\n" );
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document.write( "Edwin

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