let

l = the length of the rectangular pool, l>0

w = the width of the rectangular pool, w>0

x = 3 ft the width of the surrounding deck

the dimensions of the outside edge of the deck are: l + 2x and w + 2x

a rectangular swimming pool is 10 ft longer than it is wide

l = w + 10

the area of the pool and deck is 1,656 square feet

(l + 2x)(w + 2x) = 1656

(l + 2*3)(w + 2*3) = 1656

plug l = w + 10 into the last equation

(w + 10 + 6)(w + 6) = 1656

by solving we find

w = 30 ft

click here to see the step by step solution of the equation

l = 10 + 30

l = 40 ft

l + 2x = 40 + 2*3 = 46 ft

w + 2x = 30 + 2*3 = 36 ft

the dimensions of the outside edge of the deck are 36 ft and 46 ft.