In quadrilateral ABCD, we have AB = 3, BC = 6, CD = 4, and DA = 4.
If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.
AC divides the quadrilateral into two triangles, triangle(ABC) and triangle(ADC)
Each two sides of the triangle must have a sum greater than the third side.
In triangle(ABC), AC can be 4, 5, 6, 7, or 8
In triangle(ADC), AC can be 1, 2, 3, 4, 5, 6, or 7.
Combining the two, we get 4, 5, 6, or 7.