Refer to the illustration in the attachment.
The area of the pathway is simply the area produced by the rectangle formed with the pathway minus the area of the park.
'w' is the width of the pathway
(200 + 2w)(350 + 2w) - 200(350) = 74.464 m²
Using FOIL Method you'll have:
70,000 + 400w + 700w + 4w² - 70,000 = 74.464 m²
4w² + 1100w = 74.464
Use quadratic formula to find the values of w.
w = 0.0677 , w=-275.07
Take the positive answer.
Therefore the width of the pathway is 0.0677m