AMC 12 2006b Problem 10

In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

$\text {(A) } 43 \text {(B) } 44 \text {(C) } 45 \text {(D) } 46 \text {(E) } 47$