let
x-----------> the length of a rectangle
y-----------> the width of a rectangle
we know that
area of a rectangle =length*width
area=55 mi²
55=x*y--------> equation 1
y=x-6-------> equation 2
substitute equation 2 in equation 1
55=x*[x-6]------> 55=x²-6x----------> x²-6x-55=0
using a graph tool-----> to resolve the second order equation
see the attached figure
the solution is
x=11 mi
y=x-6-----> y=11-6-----> y=5 mi
the answer is
the length of a rectangle is 11 miles
the width of a rectangle is 5 miles
