The sides of a triangle are of length 4, and x. Determine all of the possible integer values of x such that the largest angle of the triangle is less than 90 degrees.
Case I: The longest side has length . Then forms a right triangle. So possible integral values of x here are 3 and 4.
Case II: The longest side has length . Then forms a right triangle. So the only possible integral value of x in this case is 5.
So x can be 3, 4, or 5.
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Case I: The longest side has length
. Then 
forms a right triangle. So possible integral values of x here are 3 and 4.
Case II: The longest side has length
. Then 
forms a right triangle. So the only possible integral value of x in this case is 5.
So x can be 3, 4, or 5.