Question

Your backyard is 27 feet longer than it is wide. Its area is 9718 square feet. What is the width Set up and solve a quadratic equation.

Answer 1

Answer:

Width = 86 feet

Step-by-step explanation:

Create two equations with the info:

L = 27 + W

where L represents the length and W the width of the backyard.

The other one is about the area of the rectangular backyard:

Area = L x W

where you replace the area with 9718 and the length (L) with (27 + W):

$Area= L\,*\,W\\9718=(W+27)\,W\\9718=W^2+27\,W\\W^2+27\,W-9718=0$

and solve for W using the quadratic equation:

$W=\frac{-27+/-\sqrt{27^2-4(1)(-9718)} }{2\,(1)} \\W=\frac{-27+/-\sqrt{39601}}{2} \\W=\frac{-27+/- 199}{2}$

This gives us two solutions:

W = - 113

and W = 86

We use the positive solution since this is a distance.

Therefore the width is: 86 feet