SOLUTION:

Rectangle 1(Longer Rectangle):


Length(L1)= L and Width(W1)=W

Rectangle 2: Length(L2) = L/2


Areas being same L*W1 = (L/2)* W2
=>LW=(L/2)*W2
=>W2 = L*W1/(L/2)=2W
Thus Perimeter of the shorter triangle 

= 2(Length +Breadth)
= 2(L/2+2W)=L+4W (OPTION D)