Let the width be x feet.
Then the length will be x+27 feet.
Area =(x+27)x=9718
x^2+27x=9718
x^2+27x-9718=0
x={-27+/-sqrt27^2-4(1)(-9718)}/2={-27+/-sqrt729+38872}/2
={-27+/-sqrt39601}/2={-27+/-199}/2=(-27+199)/2 or (-27-199)/2
=172/2 or -226/2
=86 or -113 (neglecting the negative value)
x=86
width =86 feet
length= 86+27=113 feet
Check : area=(length )(width)=(113)(86)=9718