let the length be x and the width be y

length = x

width = y

width is 4m less than length so

y = x-4

area is given by length*width

so 21 = x*y

21 = x(x-4)

21 = x2-4x get the equation to equal zero

x2-4x-21 = 0 factor this

(x-7)(x+3) = 0 set each part equal to zero

x-7 = 0 or x+3 = 0

x = 7 or x = -3

length can't be negative, so use x=7

substitute this back into the equation for y

y = x-4

y = 7-4

y = 3

so the width is 3m and the length is 7m