perimeter = 150
l = length
w = width
l + l + w + w = 150
l = w + 50
plug in w + 50 for l
(w + 50) + (w + 50) + w + w = 150
4w + 100 = 150
4w + 100 (-100) = 150 (-100)
4w = 50
4w/4 = 50/4
w = 12.5
l = w + 50
l = (12.5) + 50
l = 62.5
w = 12.5, l = 62.5
hope this helps