Area of a rectangle is length * width
Perimeter is the distance you would walk if you go around the rectangle, it is given as l + w + l + w = 2(l +w)
In given case 2(l+w ) = 400 or l + w = 200 or l = 200-w
Also l *w = 4700
Substitute for length from eq 1
(200-w)*w = 4700
w^2 -200w +4700 = 0
You can solve this quadratic to get the width, which will help you calculate the length.