If the perimeter of a certain rectangle is 50 units and its area is 1…

Perimeter of rectangle = 2 (l+b)

                     ⇒ 50 = 2(l+b)

                      ⇒ (l+b) = 25 

Area of rectangle = l × b

Now,

(l - b)² = (l + b)² - 4lb

⇒ (l - b)² = 25² - (4 × 114) = 625 - 456 = 169

⇒ l - b = \(\sqrt {169}\) = 13