# A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be?

##### 1 Answer

#### Explanation:

Take the width of the side walk as

#l = 32 - 2x#

and the width of the lawn becomes

#w = 24 - 2x#

The area of the lawn is

#A = l * w = (32 - 2x) * (24 - 2x) = 4x^2 -112x + 768#

This is equal to

This means that you have

#4x^2 - 112x + 768 = 425#

#4x^2 - 112x + 343 = 0#

This is a quadratic equation and you can solve it using the quadratic formula

#x_(1,2) = (-b +- sqrt(b^2 - 4 * a * c))/(2 * a)" "# , where

Out of the two values which you get for

#x_(1,2) = (-(-112) +- sqrt(7056))/(2 * 4)#

#x_(1,2) = (112 +- 84)/8 = { (color(red)(cancel(color(black)(x_1 = 24.5)))), (x_2 = 3.5) :}#

Thewidth of the sidewalk will thus be