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

"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"