Vincent is going to frame a rectangular picture with the dimensions shown :-
Length (L) = 5x+7y
Width (W) = 4x-2y
We know the formula of perimeter of rectangle is given by :-
Perimeter = 2·(length + width)
P = 2·(L+W) = 2L + 2W
P = 2·(5x+7y) + 2·(4x-2y)
P = 10x + 14y + 8x - 4y
P = 10x + 8x + 14y - 4y
P = 18x + 10y
So final answer is P = 18x + 10y.