Length of rectangle = a

Width of rectangle = b

Rectangle area = ab = 221 m²

b = 221/a

Rectangle peremeter = 2(a+b) = 60 m

(a+b) = 30

Substitute a = 221/b

(a+(221/a)) = 30

a²+221 = 30a

a² - 30a + 221 = 0

a² - 13a - 17a+ 221 = 0

a ( a - 13 ) - 17 ( a - 13 ) = 0

( a - 13 ) ( a - 17 ) = 0

( a - 13 ) = 0   and   ( a - 17 ) = 0

a = 13 and a = 17

If a = 13 then b = 221/13 = 17

(Length is greater than width.So it is false result.)

If a = 17 then b = 221/17 = 13

(Length is greater than width.So it is TRUE result.)

Solution :

Length of rectangle = 17m

Width of rectangle = 13m