let

l = the length of the garden, l>0

w = the width of the garden, w>0

A rectangular garden has perimeter 66 ft:

2(l + w) = 66 divide both sides by 2

l + w = 33

l = 33 - w

the area is 216 ft squared:

l*w = 216

plug l = 33 - w into l*w = 216

(33 - w)*w = 216

by solving we find:

w = 9 ft

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

l = 33 - 9

l = 24 ft

the dimensions of the garden are: the width is 9 feet and the length is 24 feet.