Let L be the length and W be the width.
"the width of a rectangle is half as long as the length"
W = (1/2)·L
"the rectangle has an area of 18 square feet"
A = L·W = 18
Substitute,
L·W = 18
L·(1/2)·L = 18
(L²)/2 = 18
L² = 36
L = 6 feet
then W = (1/2) · L
W = (1/2) · 6
W = 3 feet