SOLUTION: A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is N square centimeters , where N is a prime number. What is the greatest possible value of N? Cho

You can rule out choices a. 12 and c. 9 immediately because they
are not prime numbers.  You can also rule out choice d. 2, because
when two sides of a triangle are given, the third side must be greater 
than the difference of the other two sides, and 2 is equal to 6-4, and it
would have to be greater than 2.  So that only leaves b. 11, which is a
prime number.  

However, it may not be satisfactory to do it entirely by eliminating
the wrong choices.  Here is how you would find the answer if you 
had not been given any choices at all:



Area = ×base×height

N = ×6×h

N = 3h

 = sin(q)

h = 4sin(q)

And since N = 3h

N = 3×4sin(q)

N = 12sin(q)

Divide both sides by 12

 = sin(q)

The sine of an angle must be 1 or less.  Therefore the largest
prime number N could be and  be less than or equal 1 
is when N = the prime number 11.

Answer: b. 11 

Edwin