SOLUTION: A 60-Ft by 80-Ft parking lot is torn up to install a sidewalk of unirom width around it's perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the

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Question 249487: A 60-Ft by 80-Ft parking lot is torn up to install a sidewalk of unirom width around it's perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the sidewalk? Use the five step method to solve using algebra only.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the old parking lot is 60 feet by 80 feet.

let the length be 80 feet.

let the width be 60 feet.

the original area of the parking lot is 60 * 80 = 4800 square feet.

the new parking lot is going to be 2/3 * 4800 = 3200 square feet.

let x = the width of the sidewalk

this means that:

(60-x) * (80-x) = 3200

simplify by multiplying out the factors to get:

4800 - 60*x - 80*x + x^2 = 3200

simplify by combining like terms to get:

4800 - 140*x + x^2 = 3200

subtract 3200 from both sides of the equation to get:

4800 - 140*x + x^2 - 3200 = 0

simplify by combining like terms to get:

1600 - 140*x + x^2 = 0 which is the same as:

x^2 - 140*x + 1600 = 0

the standard form of a quadratic equation is:

ax^2 + bx + c = 0

in your equation:

a = 1
b = -140
c = 1600

use the quadratic formula to solve this since you can't find the factors easily by using the factor method.

the quadratic formula is:

x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29

you will get:

x = 127.4456265 or x = 12.55437353

substitute in your original equation and you will see that both answers are valid solutions to the equation.

x = 127.4456265, however, is too large to be considered since it is greater than 80 or 60.

your answer has to be:

x = 12.55437353

the dimensions of the new parking lot will be:

60 - 12.55437353 = 47.44562647 feet.

80 - 12.55437353 = 67.44562647 feet.

47.44562647 * 67.44562647 = 3200 square feet.

the answers are confirmed as good.

the answer to your problem is:

the width of the sidewalk is 12.55437353 feet.