let

w = the width of the rectangle garden

l = the length of the rectangle garden

the length of a rectangle garden is 9 feet more than it's width

l = 9 + w

A sidewalk 3 feet wide surrounds the garden covering an area of 450 square feet

(l + 2*3)(w + 2*3) - l*w = 450

(l + 6)(w + 6) - lw = 450

6(l + w) = 414

l + w = 69

by solving the system of equations

l = 9 + w

l + w = 69

we find

l = 39 ft

w = 30 ft

the dimensions of the garden are 39 ft and 30 ft.