let

w = the width of the field

l = the length of the field

P = 324 perimeter of the rectangular lacrosse field (P = 2(l + w))

the length of a lacrosse field is 18 yards less than twice it's width

l = w + 18

2(l + w) = 324

by solving the system of equation above we find

l = 90 yards

w = 72 yards

we need to find the dimensions of the defensive area

the length of the defensive area = the width of the field

the length of the defensive area is l1 = 72 yards

let w1 be the width of the defensive and

the defensive area = 7/24 the total field area

l1*w1 = (7/24) l*w

w1 = (7/24) l*w/l1

w1 = (7/24)*90*72/72

w1 = 26.25 yards

the defensive area of the field has dimensions 72 yards and 26.25 yards.