Let
x---------> length side of rectangle
y--------> width side of rectangle
we know that
area of rectangle=x*y-----> 117 cm²-------> x*y=117-------> equation 1
x=4+y-------> equation 2
substitute 2 in 1
(4+y)*y=117-----> y²+4y-117=0
using a graph tool------> to resolve the second order equation
see the attached figure
y=9 cm
x=4+y-----> x=4+9-----> x=13 cm
the answer is
the length side of rectangle is 13 cm