Your backyard is 27 feet longer than it is wide. Its area is 9718 square feet. What is the width?

Question

Set up and solve a quadratic equation.

Answer 1

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