the length of a rectangular garden is 4m more than its width determine the gardens width if the area is 117m^2

Answer 1

w(w+4)=117
w^2+4w-117=0

w=(-4+-sqrt(16+4*117))/2

w=-2+-sqrt(4+117)=-2+11=9
length then is 13

Answer 2

width --- x
length --- x+4

solve for x

x(x+4) = 117

hint: the quadratic factors nicely.