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
Sep 27, 2015

Answer:

#"width" = "3.5 m"#

Explanation:

Take the width of the side walk as #x#, so the length of the remaining lawn becomes

#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 #"425 ft"^2 -># given

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

#a# is the coefficient of #x^2 -># #4# in this case
#b# is the coefficient of #x -># #-112# in this case
#c# is the constant #-> 343# in this case

Out of the two values which you get for #x#, one will be absurd. Discard it and consider the other.

#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

#x = "3.5 m"#